Git commit 2d859c877a8bd9abbd14bc52acd6610712e0b986 by Stefan Gerlach. Committed on 01/11/2016 at 17:12. Pushed by sgerlach into branch 'frameworks'.
added first examples to handbook A +- -- doc/example-FFT_python-1024x532.png A +- -- doc/example-fourier_filter-1024x532.png A +- -- doc/example-maxima_2-1024x532.png M +657 -580 doc/index.docbook http://commits.kde.org/labplot/2d859c877a8bd9abbd14bc52acd6610712e0b986 diff --git a/doc/example-FFT_python-1024x532.png b/doc/example-FFT_python-1024x532.png new file mode 100644 index 0000000..d212c73 Binary files /dev/null and b/doc/example-FFT_python-1024x532.png differ diff --git a/doc/example-fourier_filter-1024x532.png b/doc/example-fourier_filter-1024x532.png new file mode 100644 index 0000000..b819f6a Binary files /dev/null and b/doc/example-fourier_filter-1024x532.png differ diff --git a/doc/example-maxima_2-1024x532.png b/doc/example-maxima_2-1024x532.png new file mode 100644 index 0000000..1f2af63 Binary files /dev/null and b/doc/example-maxima_2-1024x532.png differ diff --git a/doc/index.docbook b/doc/index.docbook index 37315e3..e492a15 100644 --- a/doc/index.docbook +++ b/doc/index.docbook @@ -58,8 +58,8 @@ </copyright> <legalnotice>&FDLNotice;</legalnotice> -<date>2016-10-22</date> -<releaseinfo>3.2.8</releaseinfo> +<date>2016-11-01</date> +<releaseinfo>3.3.0</releaseinfo> <abstract> <para> @@ -1326,532 +1326,6 @@ Also available through <command>labplot2 <option>-v</option></command> </sect1> </chapter> -<chapter id="parser"> -<title>Parser functions</title> -<para> -The &LabPlot; parser allows you to use following functions: -</para> - -<sect1 id="parser-normal"> -<title>Standard functions</title> - -<informaltable pgwide="1"><tgroup cols="2"> - -<thead><row><entry>Function</entry><entry>Description</entry></row></thead> - -<tbody> - -<row><entry>acos(x)</entry><entry><action>Arc cosine</action></entry></row> -<row><entry>acosh(x)</entry><entry><action>Arc hyperbolic cosine</action></entry></row> -<row><entry>asin(x)</entry><entry><action>Arcsine</action></entry></row> -<row><entry>asinh(x)</entry><entry><action>Arc hyperbolic sine</action></entry></row> -<row><entry>atan(x)</entry><entry><action>Arctangent</action></entry></row> -<row><entry>atan2(y,x)</entry><entry><action>Arctangent function of two variables</action></entry></row> -<row><entry>atanh(x)</entry><entry><action>Arc hyperbolic tangent</action></entry></row> -<row><entry>cbrt(x)</entry><entry><action>Cube root</action></entry></row> -<row><entry>ceil(x)</entry><entry><action>Truncate upward to integer</action></entry></row> -<row><entry>cos(x)</entry><entry><action>Cosine</action></entry></row> -<row><entry>cosh(x)</entry><entry><action>Hyperbolic cosine</action></entry></row> -<row><entry>exp(x)</entry><entry><action>Exponential, base e</action></entry></row> -<row><entry>expm1(x)</entry><entry><action>exp(x)-1</action></entry></row> -<row><entry>fabs(x)</entry><entry><action>Absolute value</action></entry></row> -<row><entry>gamma(x)</entry><entry><action>Gamma function</action></entry></row> -<row><entry>hypot(x,y)</entry><entry><action>Hypotenuse function √{x<superscript>2</superscript> + y<superscript>2</superscript>}</action></entry></row> -<row><entry>ln(x)</entry><entry><action>Logarithm, base e</action></entry></row> -<row><entry>log(x)</entry><entry><action>Logarithm, base e</action></entry></row> -<row><entry>log10(x)</entry><entry><action>Logarithm, base 10</action></entry></row> -<row><entry>logb(x)</entry><entry><action>Radix-independent exponent</action></entry></row> -<row><entry>pow(x,n)</entry><entry><action>power function x<superscript>n</superscript></action></entry></row> -<row><entry>rint(x)</entry><entry><action>round to nearest integer</action></entry></row> -<row><entry>round(x)</entry><entry><action>round to nearest integer</action></entry></row> -<row><entry>sin(x)</entry><entry><action>Sine</action></entry></row> -<row><entry>sinh(x)</entry><entry><action>Hyperbolic sine</action></entry></row> -<row><entry>sqrt(x)</entry><entry><action>Square root</action></entry></row> -<row><entry>tan(x)</entry><entry><action>Tangent</action></entry></row> -<row><entry>tanh(x)</entry><entry><action>Hyperbolic tangent</action></entry></row> -<row><entry>tgamma(x)</entry><entry><action>Gamma function</action></entry></row> -<row><entry>trunc(x)</entry><entry><action>Returns the greatest integer less than or equal to x</action></entry></row> - -</tbody></tgroup></informaltable> -</sect1> - -<sect1 id="parser-gsl"> -<title>Special functions</title> -<para> -For more information about the functions see the documentation of GSL. -</para> -<informaltable pgwide="1"><tgroup cols="2"> - -<thead><row><entry>Function</entry><entry>Description</entry></row></thead> - -<tbody> - -<row><entry>Ai(x)</entry><entry><action>Airy function Ai(x)</action></entry></row> -<row><entry>Bi(x)</entry><entry><action>Airy function Bi(x)</action></entry></row> -<row><entry>Ais(x)</entry><entry><action>scaled version of the Airy function S<subscript>Ai</subscript>(x)</action></entry></row> -<row><entry>Bis(x)</entry><entry><action>scaled version of the Airy function S<subscript>Bi</subscript>(x)</action></entry></row> -<row><entry>Aid(x)</entry><entry><action>Airy function derivative Ai'(x)</action></entry></row> -<row><entry>Bid(x)</entry><entry><action>Airy function derivative Bi'(x)</action></entry></row> -<row><entry>Aids(x)</entry><entry><action>derivative of the scaled Airy function S<subscript>Ai</subscript>(x)</action></entry></row> -<row><entry>Bids(x)</entry><entry><action>derivative of the scaled Airy function S<subscript>Bi</subscript>(x)</action></entry></row> -<row><entry>Ai0(s)</entry><entry><action>s-th zero of the Airy function Ai(x)</action></entry></row> -<row><entry>Bi0(s)</entry><entry><action>s-th zero of the Airy function Bi(x)</action></entry></row> -<row><entry>Aid0(s)</entry><entry><action>s-th zero of the Airy function derivative Ai'(x)</action></entry></row> -<row><entry>Bid0(s)</entry><entry><action>s-th zero of the Airy function derivative Bi'(x)</action></entry></row> -<row><entry>J0(x)</entry><entry><action>regular cylindrical Bessel function of zeroth order, J<subscript>0</subscript>(x)</action></entry></row> -<row><entry>J1(x)</entry><entry><action>regular cylindrical Bessel function of first order, J<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Jn(n,x)</entry><entry><action>regular cylindrical Bessel function of order n, J<subscript>n</subscript>(x)</action></entry></row> -<row><entry>Y0(x)</entry><entry><action>irregular cylindrical Bessel function of zeroth order, Y<subscript>0</subscript>(x)</action></entry></row> -<row><entry>Y1(x)</entry><entry><action>irregular cylindrical Bessel function of first order, Y<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Yn(n,x)</entry><entry><action>irregular cylindrical Bessel function of order n, Y<subscript>n</subscript>(x)</action></entry></row> -<row><entry>I0(x)</entry><entry><action>regular modified cylindrical Bessel function of zeroth order, I<subscript>0</subscript>(x)</action></entry></row> -<row><entry>I1(x)</entry><entry><action>regular modified cylindrical Bessel function of first order, I<subscript>1</subscript>(x)</action></entry></row> -<row><entry>In(n,x)</entry><entry><action>regular modified cylindrical Bessel function of order n, I<subscript>n</subscript>(x)</action></entry></row> -<row><entry>I0s(x)</entry><entry><action>scaled regular modified cylindrical Bessel function of zeroth order, exp (-|x|) I<subscript>0</subscript>(x)</action></entry></row> -<row><entry>I1s(x)</entry><entry><action>scaled regular modified cylindrical Bessel function of first order, exp(-|x|) I<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Ins(n,x)</entry><entry><action>scaled regular modified cylindrical Bessel function of order n, exp(-|x|) I<subscript>n</subscript>(x)</action></entry></row> -<row><entry>K0(x)</entry><entry><action>irregular modified cylindrical Bessel function of zeroth order, K<subscript>0</subscript>(x)</action></entry></row> -<row><entry>K1(x)</entry><entry><action>irregular modified cylindrical Bessel function of first order, K<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Kn(n,x)</entry><entry><action>irregular modified cylindrical Bessel function of order n, K<subscript>n</subscript>(x)</action></entry></row> -<row><entry>K0s(x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of zeroth order, exp(x) K<subscript>0</subscript>(x)</action></entry></row> -<row><entry>K1s(x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of first order, exp(x) K<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Kns(n,x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of order n, exp(x) K<subscript>n</subscript>(x)</action></entry></row> -<row><entry>j0(x)</entry><entry><action>regular spherical Bessel function of zeroth order, j<subscript>0</subscript>(x)</action></entry></row> -<row><entry>j1(x)</entry><entry><action>regular spherical Bessel function of first order, j<subscript>1</subscript>(x)</action></entry></row> -<row><entry>j2(x)</entry><entry><action>regular spherical Bessel function of second order, j<subscript>2</subscript>(x)</action></entry></row> -<row><entry>jl(l,x)</entry><entry><action>regular spherical Bessel function of order l, j<subscript>l</subscript>(x)</action></entry></row> -<row><entry>y0(x)</entry><entry><action>irregular spherical Bessel function of zeroth order, y<subscript>0</subscript>(x)</action></entry></row> -<row><entry>y1(x)</entry><entry><action>irregular spherical Bessel function of first order, y<subscript>1</subscript>(x)</action></entry></row> -<row><entry>y2(x)</entry><entry><action>irregular spherical Bessel function of second order, y<subscript>2</subscript>(x)</action></entry></row> -<row><entry>yl(l,x)</entry><entry><action>irregular spherical Bessel function of order l, y<subscript>l</subscript>(x)</action></entry></row> -<row><entry>i0s(x)</entry><entry><action>scaled regular modified spherical Bessel function of zeroth order, exp(-|x|) i<subscript>0</subscript>(x)</action></entry></row> -<row><entry>i1s(x)</entry><entry><action>scaled regular modified spherical Bessel function of first order, exp(-|x|) i<subscript>1</subscript>(x)</action></entry></row> -<row><entry>i2s(x)</entry><entry><action>scaled regular modified spherical Bessel function of second order, exp(-|x|) i<subscript>2</subscript>(x)</action></entry></row> -<row><entry>ils(l,x)</entry><entry><action>scaled regular modified spherical Bessel function of order l, exp(-|x|) i<subscript>l</subscript>(x)</action></entry></row> -<row><entry>k0s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of zeroth order, exp(x) k<subscript>0</subscript>(x)</action></entry></row> -<row><entry>k1s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of first order, exp(x) k<subscript>1</subscript>(x)</action></entry></row> -<row><entry>k2s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of second order, exp(x) k<subscript>2</subscript>(x)</action></entry></row> -<row><entry>kls(l,x)</entry><entry><action>scaled irregular modified spherical Bessel function of order l, exp(x) k<subscript>l</subscript>(x)</action></entry></row> -<row><entry>Jnu(ν,x)</entry><entry><action>regular cylindrical Bessel function of fractional order ν, J<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Ynu(ν,x)</entry><entry><action>irregular cylindrical Bessel function of fractional order ν, Y<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Inu(ν,x)</entry><entry><action>regular modified Bessel function of fractional order ν, I<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Inus(ν,x)</entry><entry><action>scaled regular modified Bessel function of fractional order ν, exp(-|x|) I<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Knu(ν,x)</entry><entry><action>irregular modified Bessel function of fractional order ν, K<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>lnKnu(ν,x)</entry><entry><action>logarithm of the irregular modified Bessel function of fractional order ν,ln(K<subscript>ν</subscript>(x))</action></entry></row> -<row><entry>Knus(ν,x)</entry><entry><action>scaled irregular modified Bessel function of fractional order ν, exp(|x|) K<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>J0_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>0</subscript>(x)</action></entry></row> -<row><entry>J1_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Jnu_0(nu,s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>clausen(x)</entry><entry><action>Clausen integral Cl<subscript>2</subscript>(x)</action></entry></row> -<row><entry>hydrogenicR_1(Z,R)</entry><entry><action>lowest-order normalized hydrogenic bound state radial wavefunction R<subscript>1</subscript> := 2Z √Z exp(-Z r)</action></entry></row> -<row><entry>hydrogenicR(n,l,Z,R)</entry><entry><action>n-th normalized hydrogenic bound state radial wavefunction</action></entry></row> -<row><entry>dawson(x)</entry><entry><action>Dawson's integral</action></entry></row> -<row><entry>D1(x)</entry><entry><action>first-order Debye function D<subscript>1</subscript>(x) = (1/x) ∫<subscript>0</subscript><superscript>x</superscript>(t/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>D2(x)</entry><entry><action>second-order Debye function D<subscript>2</subscript>(x) = (2/x<superscript>2</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>2</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>D3(x)</entry><entry><action>third-order Debye function D<subscript>3</subscript>(x) = (3/x<superscript>3</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>3</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>D4(x)</entry><entry><action>fourth-order Debye function D<subscript>4</subscript>(x) = (4/x<superscript>4</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>4</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>D5(x)</entry><entry><action>fifth-order Debye function D<subscript>5</subscript>(x) = (5/x<superscript>5</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>5</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>D6(x)</entry><entry><action>sixth-order Debye function D<subscript>6</subscript>(x) = (6/x<superscript>6</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>6</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> -<row><entry>Li2(x)</entry><entry><action>dilogarithm</action></entry></row> -<row><entry>Kc(k)</entry><entry><action>complete elliptic integral K(k)</action></entry></row> -<row><entry>Ec(k)</entry><entry><action>complete elliptic integral E(k)</action></entry></row> -<row><entry>F(phi,k)</entry><entry><action>incomplete elliptic integral F(phi,k)</action></entry></row> -<row><entry>E(phi,k)</entry><entry><action>incomplete elliptic integral E(phi,k)</action></entry></row> -<row><entry>P(phi,k,n)</entry><entry><action>incomplete elliptic integral P(phi,k,n)</action></entry></row> -<row><entry>D(phi,k,n)</entry><entry><action>incomplete elliptic integral D(phi,k,n)</action></entry></row> -<row><entry>RC(x,y)</entry><entry><action>incomplete elliptic integral RC(x,y)</action></entry></row> -<row><entry>RD(x,y,z)</entry><entry><action>incomplete elliptic integral RD(x,y,z)</action></entry></row> -<row><entry>RF(x,y,z)</entry><entry><action>incomplete elliptic integral RF(x,y,z)</action></entry></row> -<row><entry>RJ(x,y,z)</entry><entry><action>incomplete elliptic integral RJ(x,y,z,p)</action></entry></row> -<row><entry>erf(x)</entry><entry><action>error function erf(x) = 2/√π ∫<subscript>0</subscript><superscript>x</superscript> exp(-t<superscript>2</superscript>) dt</action></entry></row> -<row><entry>erfc(x)</entry><entry><action>complementary error function erfc(x) = 1 - erf(x) = 2/√π ∫<subscript>x</subscript><superscript>∞</superscript> exp(-t<superscript>2</superscript>) dt</action></entry></row> -<row><entry>log_erfc(x)</entry><entry><action>logarithm of the complementary error function log(erfc(x))</action></entry></row> -<row><entry>erf_Z(x)</entry><entry><action>Gaussian probability function Z(x) = (1/(2π)) exp(-x<superscript>2</superscript>/2)</action></entry></row> -<row><entry>erf_Q(x)</entry><entry><action>upper tail of the Gaussian probability function Q(x) = (1/(2π)) ∫<subscript>x</subscript><superscript>∞</superscript> exp(-t<superscript>2</superscript>/2) dt</action></entry></row> -<row><entry>hazard(x)</entry><entry><action>hazard function for the normal distribution</action></entry></row> -<row><entry>exp_mult(x,x)</entry><entry><action>exponentiate x and multiply by the factor y to return the product y exp(x)</action></entry></row> -<row><entry>exprel(x)</entry><entry><action>(exp(x)-1)/x using an algorithm that is accurate for small x</action></entry></row> -<row><entry>exprel2(x)</entry><entry><action>2(exp(x)-1-x)/x<superscript>2</superscript> using an algorithm that is accurate for small x</action></entry></row> -<row><entry>expreln(n,x)</entry><entry><action>n-relative exponential, which is the n-th generalization of the functions `exprel'</action></entry></row> -<row><entry>E1(x)</entry><entry><action>exponential integral E<subscript>1</subscript>(x), E<subscript>1</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t dt</action></entry></row> -<row><entry>E2(x)</entry><entry><action>second-order exponential integral E<subscript>2</subscript>(x), E<subscript>2</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t<superscript>2</superscript> dt</action></entry></row> -<row><entry>En(x)</entry><entry><action>exponential integral E_n(x) of order n, E<subscript>n</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t<superscript>n</superscript> dt)</action></entry></row> -<row><entry>Ei(x)</entry><entry><action>exponential integral E_i(x), Ei(x) := PV(∫<subscript>-x</subscript><superscript>∞</superscript> exp(-t)/t dt)</action></entry></row> -<row><entry>shi(x)</entry><entry><action>Shi(x) = ∫<subscript>0</subscript><superscript>x</superscript> sinh(t)/t dt</action></entry></row> -<row><entry>chi(x)</entry><entry><action>integral Chi(x) := Re[ γ<subscript>E</subscript> + log(x) + ∫<subscript>0</subscript><superscript>x</superscript> (cosh[t]-1)/t dt ]</action></entry></row> -<row><entry>Ei3(x)</entry><entry><action>exponential integral Ei<subscript>3</subscript>(x) = ∫<subscript>0</subscript><superscript>x</superscript> exp(-t<superscript>3</superscript>) dt for x >= 0</action></entry></row> -<row><entry>si(x)</entry><entry><action>Sine integral Si(x) = ∫<subscript>0</subscript><superscript>x</superscript> sin(t)/t dt</action></entry></row> -<row><entry>ci(x)</entry><entry><action>Cosine integral Ci(x) = -∫<subscript>x</subscript><superscript>∞</superscript> cos(t)/t dt for x > 0</action></entry></row> -<row><entry>atanint(x)</entry><entry><action>Arctangent integral AtanInt(x) = ∫<subscript>0</subscript><superscript>x</superscript> arctan(t)/t dt</action></entry></row> -<row><entry>Fm1(x)</entry><entry><action>complete Fermi-Dirac integral with an index of -1, F<subscript>-1</subscript>(x) = e<superscript>x</superscript> / (1 + e<superscript>x</superscript>)</action></entry></row> -<row><entry>F0(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 0, F<subscript>0</subscript>(x) = ln(1 + e<superscript>x</superscript>)</action></entry></row> -<row><entry>F1(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 1, F<subscript>1</subscript>(x) = ∫<subscript>0</subscript><superscript>∞</superscript> (t /(exp(t-x)+1)) dt</action></entry></row> -<row><entry>F2(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 2, F<subscript>2</subscript>(x) = (1/2) ∫<subscript>0</subscript><superscript>∞</superscript> (t<superscript>2</superscript> /(exp(t-x)+1)) dt</action></entry></row> -<row><entry>Fj(j,x)</entry><entry><action>complete Fermi-Dirac integral with an index of j, F<subscript>j</subscript>(x) = (1/Γ(j+1)) ∫<subscript>0</subscript><superscript>∞</superscript> (t<superscript>j</superscript> /(exp(t-x)+1)) dt</action></entry></row> -<row><entry>Fmhalf(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>-1/2</subscript>(x)</action></entry></row> -<row><entry>Fhalf(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>1/2</subscript>(x)</action></entry></row> -<row><entry>F3half(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>3/2</subscript>(x)</action></entry></row> -<row><entry>Finc0(x,b)</entry><entry><action>incomplete Fermi-Dirac integral with an index of zero, F<subscript>0</subscript>(x,b) = ln(1 + e<superscript>b-x</superscript>) - (b-x)</action></entry></row> -<row><entry>lngamma(x)</entry><entry><action>logarithm of the Gamma function</action></entry></row> -<row><entry>gammastar(x)</entry><entry><action>regulated Gamma Function Γ<superscript>*</superscript>(x) for x > 0</action></entry></row> -<row><entry>gammainv(x)</entry><entry><action>reciprocal of the gamma function, 1/Γ(x) using the real Lanczos method.</action></entry></row> -<row><entry>fact(n)</entry><entry><action>factorial n!</action></entry></row> -<row><entry>doublefact(n)</entry><entry><action>double factorial n!! = n(n-2)(n-4)...</action></entry></row> -<row><entry>lnfact(n)</entry><entry><action>logarithm of the factorial of n, log(n!)</action></entry></row> -<row><entry>lndoublefact(n)</entry><entry><action>logarithm of the double factorial log(n!!)</action></entry></row> -<row><entry>choose(n,m)</entry><entry><action>combinatorial factor `n choose m' = n!/(m!(n-m)!)</action></entry></row> -<row><entry>lnchoose(n,m)</entry><entry><action>logarithm of `n choose m'</action></entry></row> -<row><entry>taylor(n,x)</entry><entry><action>Taylor coefficient x<superscript>n</superscript> / n! for x >= 0, n >= 0</action></entry></row> -<row><entry>poch(a,x)</entry><entry><action>Pochhammer symbol (a)<subscript>x</subscript> := Γ(a + x)/Γ(x)</action></entry></row> -<row><entry>lnpoch(a,x)</entry><entry><action>logarithm of the Pochhammer symbol (a)<subscript>x</subscript> := Γ(a + x)/Γ(x)</action></entry></row> -<row><entry>pochrel(a,x)</entry><entry><action>relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)<subscript>x</subscript> := Γ(a + x)/Γ(a)</action></entry></row> -<row><entry>gammainc(a,x)</entry><entry><action>incomplete Gamma Function Γ(a,x) = ∫<subscript>x</subscript><superscript>∞</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> -<row><entry>gammaincQ(a,x)</entry><entry><action>normalized incomplete Gamma Function P(a,x) = 1/Γ(a) ∫<subscript>x</subscript><superscript>∞</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> -<row><entry>gammaincP(a,x)</entry><entry><action>complementary normalized incomplete Gamma Function P(a,x) = 1/Γ(a) ∫<subscript>0</subscript><superscript>x</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> -<row><entry>beta(a,b)</entry><entry><action>Beta Function, B(a,b) = Γ(a) Γ(b)/Γ(a+b) for a > 0, b > 0</action></entry></row> -<row><entry>lnbeta(a,b)</entry><entry><action>logarithm of the Beta Function, log(B(a,b)) for a > 0, b > 0</action></entry></row> -<row><entry>betainc(a,b,x)</entry><entry><action>normalize incomplete Beta function B_x(a,b)/B(a,b) for a > 0, b > 0 </action></entry></row> -<row><entry>C1(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>1</subscript>(x)</action></entry></row> -<row><entry>C2(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>2</subscript>(x)</action></entry></row> -<row><entry>C3(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>3</subscript>(x)</action></entry></row> -<row><entry>Cn(n,λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>n</subscript>(x)</action></entry></row> -<row><entry>hyperg_0F1(c,x)</entry><entry><action>hypergeometric function <subscript>0</subscript>F<subscript>1</subscript>(c,x)</action></entry></row> -<row><entry>hyperg_1F1i(m,n,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(m,n,x) = M(m,n,x) for integer parameters m, n</action></entry></row> -<row><entry>hyperg_1F1(a,b,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(a,b,x) = M(a,b,x) for general parameters a,b</action></entry></row> -<row><entry>hyperg_Ui(m,n,x)</entry><entry><action>confluent hypergeometric function U(m,n,x) for integer parameters m,n</action></entry></row> -<row><entry>hyperg_U(a,b,x)</entry><entry><action>confluent hypergeometric function U(a,b,x)</action></entry></row> -<row><entry>hyperg_2F1(a,b,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x)</action></entry></row> -<row><entry>hyperg_2F1c(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) with complex parameters</action></entry></row> -<row><entry>hyperg_2F1r(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x) / Γ(c)</action></entry></row> -<row><entry>hyperg_2F1cr(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) / Γ(c)</action></entry></row> -<row><entry>hyperg_2F0(a,b,x)</entry><entry><action>hypergeometric function <subscript>2</subscript>F<subscript>0</subscript>(a,b,x)</action></entry></row> -<row><entry>L1(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>1</subscript>(x)</action></entry></row> -<row><entry>L2(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>2</subscript>(x)</action></entry></row> -<row><entry>L3(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>3</subscript>(x)</action></entry></row> -<row><entry>W0(x)</entry><entry><action>principal branch of the Lambert W function, W<subscript>0</subscript>(x)</action></entry></row> -<row><entry>Wm1(x)</entry><entry><action>secondary real-valued branch of the Lambert W function, W<subscript>-1</subscript>(x)</action></entry></row> -<row><entry>P1(x)</entry><entry><action>Legendre polynomials P<subscript>1</subscript>(x)</action></entry></row> -<row><entry>P2(x)</entry><entry><action>Legendre polynomials P<subscript>2</subscript>(x)</action></entry></row> -<row><entry>P3(x)</entry><entry><action>Legendre polynomials P<subscript>3</subscript>(x)</action></entry></row> -<row><entry>Pl(l,x)</entry><entry><action>Legendre polynomials P<subscript>l</subscript>(x)</action></entry></row> -<row><entry>Q0(x)</entry><entry><action>Legendre polynomials Q<subscript>0</subscript>(x)</action></entry></row> -<row><entry>Q1(x)</entry><entry><action>Legendre polynomials Q<subscript>1</subscript>(x)</action></entry></row> -<row><entry>Ql(l,x)</entry><entry><action>Legendre polynomials Q<subscript>l</subscript>(x)</action></entry></row> -<row><entry>Plm(l,m,x)</entry><entry><action>associated Legendre polynomial P<subscript>l</subscript><superscript>m</superscript>(x)</action></entry></row> -<row><entry>Pslm(l,m,x)</entry><entry><action>normalized associated Legendre polynomial √{(2l+1)/(4π)} √{(l-m)!/(l+m)!} P<subscript>l</subscript><superscript>m</superscript>(x) suitable for use in spherical harmonics</action></entry></row> -<row><entry>Phalf(λ,x)</entry><entry><action>irregular Spherical Conical Function P<superscript>1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pmhalf(λ,x)</entry><entry><action>regular Spherical Conical Function P<superscript>-1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pc0(λ,x)</entry><entry><action>conical function P<superscript>0</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pc1(λ,x)</entry><entry><action>conical function P<superscript>1</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Psr(l,λ,x)</entry><entry><action>Regular Spherical Conical Function P<superscript>-1/2-l</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, l >= -1</action></entry></row> -<row><entry>Pcr(l,λ,x)</entry><entry><action>Regular Cylindrical Conical Function P<superscript>-m</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, m >= -1</action></entry></row> -<row><entry>H3d0(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>0</subscript>(λ,,η) := sin(λ η)/(λ sinh(η)) for η >= 0</action></entry></row> -<row><entry>H3d1(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>1</subscript>(λ,η) := 1/√{λ<superscript>2</superscript> + 1} sin(λ η)/(λ sinh(η)) (coth(η) - λ cot(λ η)) for η >= 0</action></entry></row> -<row><entry>H3d(l,λ,η)</entry><entry><action>L'th radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space eta >= 0, l >= 0</action></entry></row> -<row><entry>logabs(x)</entry><entry><action>logarithm of the magnitude of X, log(|x|)</action></entry></row> -<row><entry>logp(x)</entry><entry><action>log(1 + x) for x > -1 using an algorithm that is accurate for small x</action></entry></row> -<row><entry>logm(x)</entry><entry><action>log(1 + x) - x for x > -1 using an algorithm that is accurate for small x</action></entry></row> -<row><entry>psiint(n)</entry><entry><action>digamma function ψ(n) for positive integer n</action></entry></row> -<row><entry>psi(x)</entry><entry><action>digamma function ψ(n) for general x</action></entry></row> -<row><entry>psi1piy(y)</entry><entry><action>real part of the digamma function on the line 1+i y, Re[ψ(1 + i y)]</action></entry></row> -<row><entry>psi1int(n)</entry><entry><action>Trigamma function ψ'(n) for positive integer n</action></entry></row> -<row><entry>psi1(n)</entry><entry><action>Trigamma function ψ'(x) for general x</action></entry></row> -<row><entry>psin(m,x)</entry><entry><action>polygamma function ψ<superscript>(m)</superscript>(x) for m >= 0, x > 0</action></entry></row> -<row><entry>synchrotron1(x)</entry><entry><action>first synchrotron function x ∫<subscript>x</subscript><superscript>∞</superscript> K<subscript>5/3</subscript>(t) dt for x >= 0</action></entry></row> -<row><entry>synchrotron2(x)</entry><entry><action>second synchrotron function x K<subscript>2/3</subscript>(x) for x >= 0</action></entry></row> -<row><entry>J2(x)</entry><entry><action>transport function J(2,x)</action></entry></row> -<row><entry>J3(x)</entry><entry><action>transport function J(3,x)</action></entry></row> -<row><entry>J4(x)</entry><entry><action>transport function J(4,x)</action></entry></row> -<row><entry>J5(x)</entry><entry><action>transport function J(5,x)</action></entry></row> -<row><entry>sinc(x)</entry><entry><action>sinc(x) = sin(π x) / (π x)</action></entry></row> -<row><entry>logsinh(x)</entry><entry><action>log(sinh(x)) for x > 0</action></entry></row> -<row><entry>logcosh(x)</entry><entry><action>log(cosh(x))</action></entry></row> -<row><entry>anglesymm(α)</entry><entry><action>force the angle α to lie in the range (-π,π]</action></entry></row> -<row><entry>anglepos(α)</entry><entry><action>force the angle α to lie in the range (0,2π]</action></entry></row> -<row><entry>zetaint(n)</entry><entry><action>Riemann zeta function ζ(n) for integer n</action></entry></row> -<row><entry>zeta(s)</entry><entry><action>Riemann zeta function ζ(s) for arbitrary s</action></entry></row> -<row><entry>zetam1int(n)</entry><entry><action>Riemann ζ function minus 1 for integer n</action></entry></row> -<row><entry>zetam1(s)</entry><entry><action>Riemann ζ function minus 1</action></entry></row> -<row><entry>zetaintm1(s)</entry><entry><action>Riemann ζ function for integer n minus 1</action></entry></row> -<row><entry>hzeta(s,q)</entry><entry><action>Hurwitz zeta function ζ(s,q) for s > 1, q > 0</action></entry></row> -<row><entry>etaint(n)</entry><entry><action>eta function η(n) for integer n</action></entry></row> -<row><entry>eta(s)</entry><entry><action>eta function η(s) for arbitrary s</action></entry></row> -<row><entry>gsl_log1p(x)</entry><entry><action>log(1+x)</action></entry></row> -<row><entry>gsl_expm1(x)</entry><entry><action>exp(x)-1</action></entry></row> -<row><entry>gsl_hypot(x,y)</entry><entry><action>√{x<superscript>2</superscript> + y<superscript>2</superscript>}</action></entry></row> -<row><entry>gsl_acosh(x)</entry><entry><action>arccosh(x)</action></entry></row> -<row><entry>gsl_asinh(x)</entry><entry><action>arcsinh(x)</action></entry></row> -<row><entry>gsl_atanh(x)</entry><entry><action>arctanh(x)</action></entry></row> -</tbody> -</tgroup> -</informaltable> -</sect1> - -<sect1 id="parser-ran-gsl"> -<title>Random number distributions</title> -<para> -For more information about the functions see the documentation of GSL. -</para> -<informaltable pgwide="1"><tgroup cols="2"> - -<thead><row><entry>Function</entry><entry>Description</entry></row></thead> - -<tbody> - -<row><entry>gaussian(x,σ)</entry><entry><action>probability density p(x) for a Gaussian distribution with standard deviation σ</action></entry></row> -<row><entry>ugaussian(x)</entry><entry><action>unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1</action></entry></row> -<row><entry>gaussianP(x,σ)</entry><entry><action>cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ</action></entry></row> -<row><entry>gaussianQ(x,σ)</entry><entry><action>cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ</action></entry></row> -<row><entry>gaussianPinv(P,σ)</entry><entry><action>inverse cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ</action></entry></row> -<row><entry>gaussianQinv(Q,σ)</entry><entry><action>inverse cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ</action></entry></row> -<row><entry>ugaussianP(x)</entry><entry><action>cumulative distribution function P(x) for the unit Gaussian distribution</action></entry></row> -<row><entry>ugaussianQ(x)</entry><entry><action>cumulative distribution function Q(x) for the unit Gaussian distribution</action></entry></row> -<row><entry>ugaussianPinv(P)</entry><entry><action>inverse cumulative distribution function P(x) for the unit Gaussian distribution</action></entry></row> -<row><entry>ugaussianQinv(Q)</entry><entry><action>inverse cumulative distribution function Q(x) for the unit Gaussian distribution</action></entry></row> -<row><entry>gaussiantail(x,a,σ)</entry><entry><action>probability density p(x) for a Gaussian tail distribution with standard deviation σ and lower limit a</action></entry></row> -<row><entry>ugaussiantail(x,a)</entry><entry><action>tail of a unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1</action></entry></row> -<row><entry>gaussianbi(x,y,σ<subscript>x</subscript>,σ<subscript>y</subscript>,ρ)</entry><entry><action>probability density p(x,y) for a bivariate gaussian distribution - with standard deviations σ<subscript>x</subscript>, σ<subscript>y</subscript> and correlation coefficient ρ</action></entry></row> -<row><entry>exponential(x,μ)</entry><entry><action>probability density p(x) for an exponential distribution with mean μ</action></entry></row> -<row><entry>exponentialP(x,μ)</entry><entry><action>cumulative distribution function P(x) for an exponential distribution with mean μ</action></entry></row> -<row><entry>exponentialQ(x,μ)</entry><entry><action>cumulative distribution function Q(x) for an exponential distribution with mean μ</action></entry></row> -<row><entry>exponentialPinv(P,μ)</entry><entry><action>inverse cumulative distribution function P(x) for an exponential distribution with mean μ</action></entry></row> -<row><entry>exponentialQinv(Q,μ)</entry><entry><action>inverse cumulative distribution function Q(x) for an exponential distribution with mean μ</action></entry></row> -<row><entry>laplace(x,a)</entry><entry><action>probability density p(x) for a Laplace distribution with width a</action></entry></row> -<row><entry>laplaceP(x,a)</entry><entry><action>cumulative distribution function P(x) for a Laplace distribution with width a</action></entry></row> -<row><entry>laplaceQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a Laplace distribution with width a</action></entry></row> -<row><entry>laplacePinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for an Laplace distribution with width a</action></entry></row> -<row><entry>laplaceQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for an Laplace distribution with width a</action></entry></row> -<row><entry>exppow(x,a,b)</entry><entry><action>probability density p(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> -<row><entry>exppowP(x,a,b)</entry><entry><action>cumulative probability density P(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> -<row><entry>exppowQ(x,a,b)</entry><entry><action>cumulative probability density Q(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> -<row><entry>cauchy(x,a)</entry><entry><action>probability density p(x) for a Cauchy (Lorentz) distribution with scale parameter a</action></entry></row> -<row><entry>cauchyP(x,a)</entry><entry><action>cumulative distribution function P(x) for a Cauchy distribution with scale parameter a</action></entry></row> -<row><entry>cauchyQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a</action></entry></row> -<row><entry>cauchyPinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for a Cauchy distribution with scale parameter a</action></entry></row> -<row><entry>cauchyQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a</action></entry></row> -<row><entry>rayleigh(x,σ)</entry><entry><action>probability density p(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> -<row><entry>rayleighP(x,σ)</entry><entry><action>cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> -<row><entry>rayleighQ(x,σ)</entry><entry><action>cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> -<row><entry>rayleighPinv(P,σ)</entry><entry><action>inverse cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> -<row><entry>rayleighQinv(Q,σ)</entry><entry><action>inverse cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> -<row><entry>rayleigh_tail(x,a,σ)</entry><entry><action>probability density p(x) for a Rayleigh tail distribution with scale parameter σ and lower limit a</action></entry></row> -<row><entry>landau(x)</entry><entry><action>probability density p(x) for the Landau distribution</action></entry></row> -<row><entry>gammapdf(x,a,b)</entry><entry><action>probability density p(x) for a gamma distribution with parameters a and b</action></entry></row> -<row><entry>gammaP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a gamma distribution with parameters a and b</action></entry></row> -<row><entry>gammaQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a gamma distribution with parameters a and b</action></entry></row> -<row><entry>gammaPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a gamma distribution with parameters a and b</action></entry></row> -<row><entry>gammaQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a gamma distribution with parameters a and b</action></entry></row> -<row><entry>flat(x,a,b)</entry><entry><action>probability density p(x) for a uniform distribution from a to b</action></entry></row> -<row><entry>flatP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a uniform distribution from a to b</action></entry></row> -<row><entry>flatQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a uniform distribution from a to b</action></entry></row> -<row><entry>flatPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a uniform distribution from a to b</action></entry></row> -<row><entry>flatQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a uniform distribution from a to b</action></entry></row> -<row><entry>lognormal(x,ζ,σ)</entry><entry><action>probability density p(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> -<row><entry>lognormalP(x,ζ,σ)</entry><entry><action>cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> -<row><entry>lognormalQ(x,ζ,σ)</entry><entry><action>cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> -<row><entry>lognormalPinv(P,ζ,σ)</entry><entry><action>inverse cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> -<row><entry>lognormalQinv(Q,ζ,σ)</entry><entry><action>inverse cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> -<row><entry>chisq(x,ν)</entry><entry><action>probability density p(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> -<row><entry>chisqP(x,ν)</entry><entry><action>cumulative distribution function P(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> -<row><entry>chisqQ(x,ν)</entry><entry><action>cumulative distribution function Q(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> -<row><entry>chisqPinv(P,ν)</entry><entry><action>inverse cumulative distribution function P(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> -<row><entry>chisqQinv(Q,ν)</entry><entry><action>inverse cumulative distribution function Q(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> -<row><entry>fdist(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>probability density p(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> -<row><entry>fdistP(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>cumulative distribution function P(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> -<row><entry>fdistQ(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>cumulative distribution function Q(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> -<row><entry>fdistPinv(P,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>inverse cumulative distribution function P(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> -<row><entry>fdistQinv(Q,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>inverse cumulative distribution function Q(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> -<row><entry>tdist(x,ν)</entry><entry><action>probability density p(x) for a t-distribution with ν degrees of freedom</action></entry></row> -<row><entry>tdistP(x,ν)</entry><entry><action>cumulative distribution function P(x) for a t-distribution with ν degrees of freedom</action></entry></row> -<row><entry>tdistQ(x,ν)</entry><entry><action>cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom</action></entry></row> -<row><entry>tdistPinv(P,ν)</entry><entry><action>inverse cumulative distribution function P(x) for a t-distribution with ν degrees of freedom</action></entry></row> -<row><entry>tdistQinv(Q,ν)</entry><entry><action>inverse cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom</action></entry></row> -<row><entry>betapdf(x,a,b)</entry><entry><action>probability density p(x) for a beta distribution with parameters a and b</action></entry></row> -<row><entry>betaP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a beta distribution with parameters a and b</action></entry></row> -<row><entry>betaQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a beta distribution with parameters a and b</action></entry></row> -<row><entry>betaPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a beta distribution with parameters a and b</action></entry></row> -<row><entry>betaQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a beta distribution with parameters a and b</action></entry></row> -<row><entry>logistic(x,a)</entry><entry><action>probability density p(x) for a logistic distribution with scale parameter a</action></entry></row> -<row><entry>logisticP(x,a)</entry><entry><action>cumulative distribution function P(x) for a logistic distribution with scale parameter a</action></entry></row> -<row><entry>logisticQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a logistic distribution with scale parameter a</action></entry></row> -<row><entry>logisticPinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for a logistic distribution with scale parameter a</action></entry></row> -<row><entry>logisticQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for a logistic distribution with scale parameter a</action></entry></row> -<row><entry>pareto(x,a,b)</entry><entry><action>probability density p(x) for a Pareto distribution with exponent a and scale b</action></entry></row> -<row><entry>paretoP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b</action></entry></row> -<row><entry>paretoQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b</action></entry></row> -<row><entry>paretoPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b</action></entry></row> -<row><entry>paretoQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b</action></entry></row> -<row><entry>weibull(x,a,b)</entry><entry><action>probability density p(x) for a Weibull distribution with scale a and exponent b</action></entry></row> -<row><entry>weibullP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b</action></entry></row> -<row><entry>weibullQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b</action></entry></row> -<row><entry>weibullPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b</action></entry></row> -<row><entry>weibullQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b</action></entry></row> -<row><entry>gumbel1(x,a,b)</entry><entry><action>probability density p(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel1P(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel1Q(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel1Pinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel1Qinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel2(x,a,b)</entry><entry><action>probability density p(x) at X for a Type-2 Gumbel distribution with parameters A and B</action></entry></row> -<row><entry>gumbel2P(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel2Q(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel2Pinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>gumbel2Qinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> -<row><entry>poisson(k,μ)</entry><entry><action>probability p(k) of obtaining k from a Poisson distribution with mean μ</action></entry></row> -<row><entry>poissonP(k,μ)</entry><entry><action>cumulative distribution functions P(k) for a Poisson distribution with mean μ</action></entry></row> -<row><entry>poissonQ(k,μ)</entry><entry><action>cumulative distribution functions Q(k) for a Poisson distribution with mean μ</action></entry></row> -<row><entry>bernoulli(k,p)</entry><entry><action>probability p(k) of obtaining k from a Bernoulli distribution with probability parameter p</action></entry></row> -<row><entry>binomial(k,p,n)</entry><entry><action>probability p(k) of obtaining p from a binomial distribution with parameters p and n</action></entry></row> -<row><entry>binomialP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a binomial distribution with parameters p and n</action></entry></row> -<row><entry>binomialQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a binomial distribution with parameters p and n</action></entry></row> -<row><entry>nbinomial(k,p,n)</entry><entry><action>probability p(k) of obtaining k from a negative binomial distribution with parameters p and n</action></entry></row> -<row><entry>nbinomialP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a negative binomial distribution with parameters p and n</action></entry></row> -<row><entry>nbinomialQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a negative binomial distribution with parameters p and n</action></entry></row> -<row><entry>pascal(k,p,n)</entry><entry><action>probability p(k) of obtaining k from a Pascal distribution with parameters p and n</action></entry></row> -<row><entry>pascalP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a Pascal distribution with parameters p and n</action></entry></row> -<row><entry>pascalQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a Pascal distribution with parameters p and n</action></entry></row> -<row><entry>geometric(k,p)</entry><entry><action>probability p(k) of obtaining k from a geometric distribution with probability parameter p</action></entry></row> -<row><entry>geometricP(k,p)</entry><entry><action>cumulative distribution functions P(k) for a geometric distribution with parameter p</action></entry></row> -<row><entry>geometricQ(k,p)</entry><entry><action>cumulative distribution functions Q(k) for a geometric distribution with parameter p</action></entry></row> -<row><entry>hypergeometric(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>probability p(k) of obtaining k from a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> -<row><entry>hypergeometricP(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>cumulative distribution function P(k) for a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> -<row><entry>hypergeometricQ(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>cumulative distribution function Q(k) for a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> -<row><entry>logarithmic(k,p)</entry><entry><action>probability p(k) of obtaining K from a logarithmic distribution with probability parameter p</action></entry></row> -</tbody> -</tgroup> -</informaltable> -</sect1> - -<sect1 id="parser-const"> -<title>Constants</title> - -<informaltable pgwide="1"><tgroup cols="2"> - -<thead><row><entry>Constant</entry><entry>Description</entry></row></thead> - -<tbody> - -<row><entry>e</entry><entry><action>The base of natural logarithms</action></entry></row> -<row><entry>pi</entry><entry><action>π</action></entry></row> - -</tbody></tgroup></informaltable> -</sect1> - -<sect1 id="parser-const-gsl"> -<title>GSL constants</title> -<para> -For more information about this constants see the documentation of GSL. -</para> -<informaltable pgwide="1"><tgroup cols="2"> - -<thead><row><entry>Constant</entry><entry>Description</entry></row></thead> - -<tbody> - -<row><entry>c</entry><entry><action> The speed of light in vacuum</action></entry></row> -<row><entry>mu0</entry><entry><action>The permeability of free space</action></entry></row> -<row><entry>e0</entry><entry><action>The permittivity of free space</action></entry></row> -<row><entry>h</entry><entry><action>The Planck constant h</action></entry></row> -<row><entry>hbar</entry><entry><action>The reduced Planck constant ℏ</action></entry></row> -<row><entry>na</entry><entry><action>Avogadro's number</action></entry></row> -<row><entry>f</entry><entry><action>The molar charge of 1 Faraday</action></entry></row> -<row><entry>k</entry><entry><action>The Boltzmann constant</action></entry></row> -<row><entry>r0</entry><entry><action>The molar gas constant</action></entry></row> -<row><entry>v0</entry><entry><action>The standard gas volume</action></entry></row> -<row><entry>sigma</entry><entry><action>The Stefan–Boltzmann constant</action></entry></row> -<row><entry>gauss</entry><entry><action>The magnetic field of 1 Gauss</action></entry></row> -<row><entry>au</entry><entry><action>The length of 1 astronomical unit (mean earth-sun distance)</action></entry></row> -<row><entry>G</entry><entry><action>The gravitational constant</action></entry></row> -<row><entry>ly</entry><entry><action>The distance of 1 light-year</action></entry></row> -<row><entry>pc</entry><entry><action>The distance of 1 parsec</action></entry></row> -<row><entry>gg</entry><entry><action>The standard gravitational acceleration on Earth</action></entry></row> -<row><entry>ms</entry><entry><action>The mass of the Sun</action></entry></row> -<row><entry>ee</entry><entry><action>The charge of the electron</action></entry></row> -<row><entry>eV</entry><entry><action>The energy of 1 electron volt</action></entry></row> -<row><entry>amu</entry><entry><action>The unified atomic mass</action></entry></row> -<row><entry>me</entry><entry><action>The mass of the electron</action></entry></row> -<row><entry>mmu</entry><entry><action>The mass of the muon</action></entry></row> -<row><entry>mp</entry><entry><action>The mass of the proton</action></entry></row> -<row><entry>mn</entry><entry><action>The mass of the neutron</action></entry></row> -<row><entry>alpha</entry><entry><action>The electromagnetic fine structure constant</action></entry></row> -<row><entry>ry</entry><entry><action>The Rydberg constant</action></entry></row> -<row><entry>a0</entry><entry><action>The Bohr radius</action></entry></row> -<row><entry>a</entry><entry><action>The length of 1 angstrom</action></entry></row> -<row><entry>barn</entry><entry><action> The area of 1 barn</action></entry></row> -<row><entry>muB</entry><entry><action>The Bohr Magneton</action></entry></row> -<row><entry>mun</entry><entry><action>The Nuclear Magneton</action></entry></row> -<row><entry>mue</entry><entry><action>The magnetic moment of the electron</action></entry></row> -<row><entry>mup</entry><entry><action>The magnetic moment of the proton</action></entry></row> -<row><entry>sigmaT</entry><entry><action>The Thomson cross section for an electron</action></entry></row> -<row><entry>pD</entry><entry><action>The debye</action></entry></row> -<row><entry>min</entry><entry><action>The number of seconds in 1 minute</action></entry></row> -<row><entry>h</entry><entry><action>The number of seconds in 1 hour</action></entry></row> -<row><entry>d</entry><entry><action> The number of seconds in 1 day</action></entry></row> -<row><entry>week</entry><entry><action>The number of seconds in 1 week</action></entry></row> -<row><entry>in</entry><entry><action>The length of 1 inch</action></entry></row> -<row><entry>ft</entry><entry><action>The length of 1 foot</action></entry></row> -<row><entry>yard</entry><entry><action>The length of 1 yard</action></entry></row> -<row><entry>mil</entry><entry><action>The length of 1 mil (1/1000th of an inch)</action></entry></row> -<row><entry>v_km_per_h</entry><entry><action>The speed of 1 kilometer per hour</action></entry></row> -<row><entry>v_mile_per_h</entry><entry><action>The speed of 1 mile per hour</action></entry></row> -<row><entry>nmile</entry><entry><action>The length of 1 nautical mile</action></entry></row> -<row><entry>fathom</entry><entry><action>The length of 1 fathom</action></entry></row> -<row><entry>knot</entry><entry><action>The speed of 1 knot</action></entry></row> -<row><entry>pt</entry><entry><action> The length of 1 printer's point (1/72 inch)</action></entry></row> -<row><entry>texpt</entry><entry><action>The length of 1 TeX point (1/72.27 inch)</action></entry></row> -<row><entry>micron</entry><entry><action>The length of 1 micrometre</action></entry></row> -<row><entry>hectare</entry><entry><action>The area of 1 hectare</action></entry></row> -<row><entry>acre</entry><entry><action>The area of 1 acre</action></entry></row> -<row><entry>liter</entry><entry><action>The volume of 1 liter</action></entry></row> -<row><entry>us_gallon</entry><entry><action>The volume of 1 US gallon</action></entry></row> -<row><entry>can_gallon</entry><entry><action>The volume of 1 Canadian gallon</action></entry></row> -<row><entry>uk_gallon</entry><entry><action>The volume of 1 UK gallon</action></entry></row> -<row><entry>quart</entry><entry><action>The volume of 1 quart</action></entry></row> -<row><entry>pint</entry><entry><action>The volume of 1 pint</action></entry></row> -<row><entry>pound</entry><entry><action>The mass of 1 pound</action></entry></row> -<row><entry>ounce</entry><entry><action>The mass of 1 ounce</action></entry></row> -<row><entry>ton</entry><entry><action>The mass of 1 ton</action></entry></row> -<row><entry>mton</entry><entry><action>The mass of 1 metric ton (1000 kg)</action></entry></row> -<row><entry>uk_ton</entry><entry><action>The mass of 1 UK ton</action></entry></row> -<row><entry>troy_ounce</entry><entry><action>The mass of 1 troy ounce</action></entry></row> -<row><entry>carat</entry><entry><action>The mass of 1 carat</action></entry></row> -<row><entry>gram_force</entry><entry><action>The force of 1 gram weight</action></entry></row> -<row><entry>pound_force</entry><entry><action>The force of 1 pound weight</action></entry></row> -<row><entry>kilepound_force</entry><entry><action>The force of 1 kilopound weight</action></entry></row> -<row><entry>poundal</entry><entry><action>The force of 1 poundal</action></entry></row> -<row><entry>cal</entry><entry><action>The energy of 1 calorie</action></entry></row> -<row><entry>btu</entry><entry><action>The energy of 1 British Thermal Unit</action></entry></row> -<row><entry>therm</entry><entry><action>The energy of 1 Therm</action></entry></row> -<row><entry>hp</entry><entry><action>The power of 1 horsepower</action></entry></row> -<row><entry>bar</entry><entry><action>The pressure of 1 bar</action></entry></row> -<row><entry>atm</entry><entry><action>The pressure of 1 standard atmosphere</action></entry></row> -<row><entry>torr</entry><entry><action>The pressure of 1 torr</action></entry></row> -<row><entry>mhg</entry><entry><action>The pressure of 1 meter of mercury</action></entry></row> -<row><entry>inhg</entry><entry><action>The pressure of 1 inch of mercury</action></entry></row> -<row><entry>inh2o</entry><entry><action>The pressure of 1 inch of water</action></entry></row> -<row><entry>psi</entry><entry><action>The pressure of 1 pound per square inch</action></entry></row> -<row><entry>poise</entry><entry><action>The dynamic viscosity of 1 poise</action></entry></row> -<row><entry>stokes</entry><entry><action>The kinematic viscosity of 1 stokes</action></entry></row> -<row><entry>stilb</entry><entry><action>The luminance of 1 stilb</action></entry></row> -<row><entry>lumen</entry><entry><action>The luminous flux of 1 lumen</action></entry></row> -<row><entry>lux</entry><entry><action>The illuminance of 1 lux</action></entry></row> -<row><entry>phot</entry><entry><action>The illuminance of 1 phot</action></entry></row> -<row><entry>ftcandle</entry><entry><action>The illuminance of 1 footcandle</action></entry></row> -<row><entry>lambert</entry><entry><action>The luminance of 1 lambert</action></entry></row> -<row><entry>ftlambert</entry><entry><action>The luminance of 1 footlambert</action></entry></row> -<row><entry>curie</entry><entry><action>The activity of 1 curie</action></entry></row> -<row><entry>roentgen</entry><entry><action>The exposure of 1 roentgen</action></entry></row> -<row><entry>rad</entry><entry><action>The absorbed dose of 1 rad</action></entry></row> -<row><entry>N</entry><entry><action>The force of 1 newton</action></entry></row> -<row><entry>dyne</entry><entry><action>The force of 1 dyne</action></entry></row> -<row><entry>J</entry><entry><action>The energy of 1 joule</action></entry></row> -<row><entry>erg</entry><entry><action>The energy of 1 erg</action></entry></row> - -</tbody></tgroup></informaltable> - -</sect1> - -</chapter> <!-- TODO: @@ -2220,6 +1694,82 @@ data sources for the curves, add legends, export everything to pdf) would also h </sect1> </chapter> +<chapter id="examples"> +<title>Examples</title> +<sect1 id="example-2d-plotting"> + <title>2D Plotting</title> + <para>Coming soon ... + </para> + </sect1> +<sect1 id="example-signal"> + <title>Signal processing</title> + <para> + </para> + <variablelist> + <varlistentry> + <term>Fourier filter</term> + <listitem> + <para>A time signal containing Morse code is Fourier transformed to frequency space to see the main component. By applying a narrow band pass filter the Morse signal is extracted and a nice ‘SOS’ can be seen: + </para> + + <screenshot> + <mediaobject><imageobject><imagedata fileref="example-fourier_filter-1024x532.png"/> + </imageobject></mediaobject> + </screenshot> + + </listitem> + </varlistentry> + </variablelist> + </sect1> +<sect1 id="example-computing"> + <title>Computing</title> + <para> + </para> + <variablelist> + <varlistentry> + <term>Maxima</term> + <listitem> + <para>Maxima session showing the chaotic dynamics of the Duffing oscillator. + The differential equation of the forced oscillator are solved with Maxima. + Plots of the trajectory, the phase space of the oscillator and the corresponding Poincaré map are done with LabPlot: + </para> + + <screenshot> + <mediaobject><imageobject><imagedata fileref="example-maxima_2-1024x532.png"/> + </imageobject></mediaobject> + </screenshot> + + </listitem> + </varlistentry> + <varlistentry> + <term>Python</term> + <listitem> + <para>Python session illustrating the effect of Blackman windowing on the Fourier transform: + </para> + + <screenshot> + <mediaobject><imageobject><imagedata fileref="example-FFT_python-1024x532.png"/> + </imageobject></mediaobject> + </screenshot> + + </listitem> + </varlistentry> + </variablelist> + </sect1> +<sect1 id="example-import-export"> + <title>Import/Export</title> + <para>Coming soon ... + </para> + </sect1> +<sect1 id="example-tools"> + <title>Tools</title> + <para>Coming soon ... + </para> + </sect1> + +</chapter> + + <chapter id="faq"> <title>Questions and Answers</title> @@ -2308,82 +1858,609 @@ needs a lot of work. <chapter id="license"> -<title>License</title> +<title>License</title> + +<para>&LabPlot;</para> +<para> +Program copyright © 2007-2016 Stefan Gerlach <email>[email protected]</email> +Program copyright © 2008-2016 Alexander Semke <email>[email protected]</email> +</para> + +<important> +<para> +&LabPlot; is still under development. There is a long list of missing features that will be implemented in later versions of &LabPlot;. +</para> +</important> + +<para> +Because there are a lot things to do, developers need every help you can give. Any contribution like wishes, corrections, +patches, bug reports or screen shots is welcome. +</para> + +<para> +Documentation copyright © 2007-2016 Stefan Gerlach +<email>[email protected]</email> + +Documentation copyright © 2008-2015 Alexander Semke +<email>[email protected]</email> + +Documentation copyright © 2014 Yuri Chornoivan +<email>[email protected]</email> +</para> + +<!-- TRANS:CREDIT_FOR_TRANSLATORS --> + +&underFDL; +&underGPL; + +</chapter> + +<appendix id="installation"> +<title>Installation</title> + +<sect1 id="getting-labplot"> +<title>How to Obtain &LabPlot;</title> + +<para> +&LabPlot; can be found on its homepage at sourceforge.net: +<ulink url="http://labplot.sf.net";>http://labplot.sf.net</ulink>. +There is an overview about all available packages at +<ulink url="http://labplot.wiki.sourceforge.net/Download";>http://labplot.wiki.sourceforge.net/Download</ulink>. +bug-fixed packages are released regular and can be found there too. +</para> +</sect1> + +<sect1 id="requirements"> +<title>Requirements</title> + +<para> +In order to successfully use &LabPlot;, you need at least a standard &Qt; 5 and &kde; KF5 installation, the &GNU; scientific library (GSL), &cantor; libcantor library. +</para> + +<!-- <para> +Optional &LabPlot; uses the following programs/libraries when available: +</para> + +<itemizedlist> +<listitem><para> +&GNU; scientific library (GSL) : used for special functions in the parser and most of the analysis functions. +</para></listitem> +</itemizedlist> +--> + +</sect1> + +<sect1 id="compilation"> +<title>Compilation and Installation</title> + +&install.compile.documentation; + +</sect1> + +</appendix> + +<appendix id="parser"> +<title>Parser functions</title> +<para> +The &LabPlot; parser allows you to use following functions: +</para> + +<sect1 id="parser-normal"> +<title>Standard functions</title> + +<informaltable pgwide="1"><tgroup cols="2"> + +<thead><row><entry>Function</entry><entry>Description</entry></row></thead> + +<tbody> + +<row><entry>acos(x)</entry><entry><action>Arc cosine</action></entry></row> +<row><entry>acosh(x)</entry><entry><action>Arc hyperbolic cosine</action></entry></row> +<row><entry>asin(x)</entry><entry><action>Arcsine</action></entry></row> +<row><entry>asinh(x)</entry><entry><action>Arc hyperbolic sine</action></entry></row> +<row><entry>atan(x)</entry><entry><action>Arctangent</action></entry></row> +<row><entry>atan2(y,x)</entry><entry><action>Arctangent function of two variables</action></entry></row> +<row><entry>atanh(x)</entry><entry><action>Arc hyperbolic tangent</action></entry></row> +<row><entry>cbrt(x)</entry><entry><action>Cube root</action></entry></row> +<row><entry>ceil(x)</entry><entry><action>Truncate upward to integer</action></entry></row> +<row><entry>cos(x)</entry><entry><action>Cosine</action></entry></row> +<row><entry>cosh(x)</entry><entry><action>Hyperbolic cosine</action></entry></row> +<row><entry>exp(x)</entry><entry><action>Exponential, base e</action></entry></row> +<row><entry>expm1(x)</entry><entry><action>exp(x)-1</action></entry></row> +<row><entry>fabs(x)</entry><entry><action>Absolute value</action></entry></row> +<row><entry>gamma(x)</entry><entry><action>Gamma function</action></entry></row> +<row><entry>hypot(x,y)</entry><entry><action>Hypotenuse function √{x<superscript>2</superscript> + y<superscript>2</superscript>}</action></entry></row> +<row><entry>ln(x)</entry><entry><action>Logarithm, base e</action></entry></row> +<row><entry>log(x)</entry><entry><action>Logarithm, base e</action></entry></row> +<row><entry>log10(x)</entry><entry><action>Logarithm, base 10</action></entry></row> +<row><entry>logb(x)</entry><entry><action>Radix-independent exponent</action></entry></row> +<row><entry>pow(x,n)</entry><entry><action>power function x<superscript>n</superscript></action></entry></row> +<row><entry>rint(x)</entry><entry><action>round to nearest integer</action></entry></row> +<row><entry>round(x)</entry><entry><action>round to nearest integer</action></entry></row> +<row><entry>sin(x)</entry><entry><action>Sine</action></entry></row> +<row><entry>sinh(x)</entry><entry><action>Hyperbolic sine</action></entry></row> +<row><entry>sqrt(x)</entry><entry><action>Square root</action></entry></row> +<row><entry>tan(x)</entry><entry><action>Tangent</action></entry></row> +<row><entry>tanh(x)</entry><entry><action>Hyperbolic tangent</action></entry></row> +<row><entry>tgamma(x)</entry><entry><action>Gamma function</action></entry></row> +<row><entry>trunc(x)</entry><entry><action>Returns the greatest integer less than or equal to x</action></entry></row> + +</tbody></tgroup></informaltable> +</sect1> -<para>&LabPlot;</para> +<sect1 id="parser-gsl"> +<title>Special functions</title> <para> -Program copyright © 2007-2016 Stefan Gerlach <email>[email protected]</email> -Program copyright © 2008-2016 Alexander Semke <email>[email protected]</email> +For more information about the functions see the documentation of GSL. </para> +<informaltable pgwide="1"><tgroup cols="2"> -<important> -<para> -&LabPlot; is still under development. There is a long list of missing features that will be implemented in later versions of &LabPlot;. -</para> -</important> +<thead><row><entry>Function</entry><entry>Description</entry></row></thead> + +<tbody> + +<row><entry>Ai(x)</entry><entry><action>Airy function Ai(x)</action></entry></row> +<row><entry>Bi(x)</entry><entry><action>Airy function Bi(x)</action></entry></row> +<row><entry>Ais(x)</entry><entry><action>scaled version of the Airy function S<subscript>Ai</subscript>(x)</action></entry></row> +<row><entry>Bis(x)</entry><entry><action>scaled version of the Airy function S<subscript>Bi</subscript>(x)</action></entry></row> +<row><entry>Aid(x)</entry><entry><action>Airy function derivative Ai'(x)</action></entry></row> +<row><entry>Bid(x)</entry><entry><action>Airy function derivative Bi'(x)</action></entry></row> +<row><entry>Aids(x)</entry><entry><action>derivative of the scaled Airy function S<subscript>Ai</subscript>(x)</action></entry></row> +<row><entry>Bids(x)</entry><entry><action>derivative of the scaled Airy function S<subscript>Bi</subscript>(x)</action></entry></row> +<row><entry>Ai0(s)</entry><entry><action>s-th zero of the Airy function Ai(x)</action></entry></row> +<row><entry>Bi0(s)</entry><entry><action>s-th zero of the Airy function Bi(x)</action></entry></row> +<row><entry>Aid0(s)</entry><entry><action>s-th zero of the Airy function derivative Ai'(x)</action></entry></row> +<row><entry>Bid0(s)</entry><entry><action>s-th zero of the Airy function derivative Bi'(x)</action></entry></row> +<row><entry>J0(x)</entry><entry><action>regular cylindrical Bessel function of zeroth order, J<subscript>0</subscript>(x)</action></entry></row> +<row><entry>J1(x)</entry><entry><action>regular cylindrical Bessel function of first order, J<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Jn(n,x)</entry><entry><action>regular cylindrical Bessel function of order n, J<subscript>n</subscript>(x)</action></entry></row> +<row><entry>Y0(x)</entry><entry><action>irregular cylindrical Bessel function of zeroth order, Y<subscript>0</subscript>(x)</action></entry></row> +<row><entry>Y1(x)</entry><entry><action>irregular cylindrical Bessel function of first order, Y<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Yn(n,x)</entry><entry><action>irregular cylindrical Bessel function of order n, Y<subscript>n</subscript>(x)</action></entry></row> +<row><entry>I0(x)</entry><entry><action>regular modified cylindrical Bessel function of zeroth order, I<subscript>0</subscript>(x)</action></entry></row> +<row><entry>I1(x)</entry><entry><action>regular modified cylindrical Bessel function of first order, I<subscript>1</subscript>(x)</action></entry></row> +<row><entry>In(n,x)</entry><entry><action>regular modified cylindrical Bessel function of order n, I<subscript>n</subscript>(x)</action></entry></row> +<row><entry>I0s(x)</entry><entry><action>scaled regular modified cylindrical Bessel function of zeroth order, exp (-|x|) I<subscript>0</subscript>(x)</action></entry></row> +<row><entry>I1s(x)</entry><entry><action>scaled regular modified cylindrical Bessel function of first order, exp(-|x|) I<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Ins(n,x)</entry><entry><action>scaled regular modified cylindrical Bessel function of order n, exp(-|x|) I<subscript>n</subscript>(x)</action></entry></row> +<row><entry>K0(x)</entry><entry><action>irregular modified cylindrical Bessel function of zeroth order, K<subscript>0</subscript>(x)</action></entry></row> +<row><entry>K1(x)</entry><entry><action>irregular modified cylindrical Bessel function of first order, K<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Kn(n,x)</entry><entry><action>irregular modified cylindrical Bessel function of order n, K<subscript>n</subscript>(x)</action></entry></row> +<row><entry>K0s(x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of zeroth order, exp(x) K<subscript>0</subscript>(x)</action></entry></row> +<row><entry>K1s(x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of first order, exp(x) K<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Kns(n,x)</entry><entry><action>scaled irregular modified cylindrical Bessel function of order n, exp(x) K<subscript>n</subscript>(x)</action></entry></row> +<row><entry>j0(x)</entry><entry><action>regular spherical Bessel function of zeroth order, j<subscript>0</subscript>(x)</action></entry></row> +<row><entry>j1(x)</entry><entry><action>regular spherical Bessel function of first order, j<subscript>1</subscript>(x)</action></entry></row> +<row><entry>j2(x)</entry><entry><action>regular spherical Bessel function of second order, j<subscript>2</subscript>(x)</action></entry></row> +<row><entry>jl(l,x)</entry><entry><action>regular spherical Bessel function of order l, j<subscript>l</subscript>(x)</action></entry></row> +<row><entry>y0(x)</entry><entry><action>irregular spherical Bessel function of zeroth order, y<subscript>0</subscript>(x)</action></entry></row> +<row><entry>y1(x)</entry><entry><action>irregular spherical Bessel function of first order, y<subscript>1</subscript>(x)</action></entry></row> +<row><entry>y2(x)</entry><entry><action>irregular spherical Bessel function of second order, y<subscript>2</subscript>(x)</action></entry></row> +<row><entry>yl(l,x)</entry><entry><action>irregular spherical Bessel function of order l, y<subscript>l</subscript>(x)</action></entry></row> +<row><entry>i0s(x)</entry><entry><action>scaled regular modified spherical Bessel function of zeroth order, exp(-|x|) i<subscript>0</subscript>(x)</action></entry></row> +<row><entry>i1s(x)</entry><entry><action>scaled regular modified spherical Bessel function of first order, exp(-|x|) i<subscript>1</subscript>(x)</action></entry></row> +<row><entry>i2s(x)</entry><entry><action>scaled regular modified spherical Bessel function of second order, exp(-|x|) i<subscript>2</subscript>(x)</action></entry></row> +<row><entry>ils(l,x)</entry><entry><action>scaled regular modified spherical Bessel function of order l, exp(-|x|) i<subscript>l</subscript>(x)</action></entry></row> +<row><entry>k0s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of zeroth order, exp(x) k<subscript>0</subscript>(x)</action></entry></row> +<row><entry>k1s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of first order, exp(x) k<subscript>1</subscript>(x)</action></entry></row> +<row><entry>k2s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of second order, exp(x) k<subscript>2</subscript>(x)</action></entry></row> +<row><entry>kls(l,x)</entry><entry><action>scaled irregular modified spherical Bessel function of order l, exp(x) k<subscript>l</subscript>(x)</action></entry></row> +<row><entry>Jnu(ν,x)</entry><entry><action>regular cylindrical Bessel function of fractional order ν, J<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Ynu(ν,x)</entry><entry><action>irregular cylindrical Bessel function of fractional order ν, Y<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Inu(ν,x)</entry><entry><action>regular modified Bessel function of fractional order ν, I<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Inus(ν,x)</entry><entry><action>scaled regular modified Bessel function of fractional order ν, exp(-|x|) I<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Knu(ν,x)</entry><entry><action>irregular modified Bessel function of fractional order ν, K<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>lnKnu(ν,x)</entry><entry><action>logarithm of the irregular modified Bessel function of fractional order ν,ln(K<subscript>ν</subscript>(x))</action></entry></row> +<row><entry>Knus(ν,x)</entry><entry><action>scaled irregular modified Bessel function of fractional order ν, exp(|x|) K<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>J0_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>0</subscript>(x)</action></entry></row> +<row><entry>J1_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Jnu_0(nu,s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>clausen(x)</entry><entry><action>Clausen integral Cl<subscript>2</subscript>(x)</action></entry></row> +<row><entry>hydrogenicR_1(Z,R)</entry><entry><action>lowest-order normalized hydrogenic bound state radial wavefunction R<subscript>1</subscript> := 2Z √Z exp(-Z r)</action></entry></row> +<row><entry>hydrogenicR(n,l,Z,R)</entry><entry><action>n-th normalized hydrogenic bound state radial wavefunction</action></entry></row> +<row><entry>dawson(x)</entry><entry><action>Dawson's integral</action></entry></row> +<row><entry>D1(x)</entry><entry><action>first-order Debye function D<subscript>1</subscript>(x) = (1/x) ∫<subscript>0</subscript><superscript>x</superscript>(t/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>D2(x)</entry><entry><action>second-order Debye function D<subscript>2</subscript>(x) = (2/x<superscript>2</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>2</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>D3(x)</entry><entry><action>third-order Debye function D<subscript>3</subscript>(x) = (3/x<superscript>3</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>3</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>D4(x)</entry><entry><action>fourth-order Debye function D<subscript>4</subscript>(x) = (4/x<superscript>4</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>4</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>D5(x)</entry><entry><action>fifth-order Debye function D<subscript>5</subscript>(x) = (5/x<superscript>5</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>5</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>D6(x)</entry><entry><action>sixth-order Debye function D<subscript>6</subscript>(x) = (6/x<superscript>6</superscript>) ∫<subscript>0</subscript><superscript>x</superscript> (t<superscript>6</superscript>/(e<superscript>t</superscript> - 1)) dt</action></entry></row> +<row><entry>Li2(x)</entry><entry><action>dilogarithm</action></entry></row> +<row><entry>Kc(k)</entry><entry><action>complete elliptic integral K(k)</action></entry></row> +<row><entry>Ec(k)</entry><entry><action>complete elliptic integral E(k)</action></entry></row> +<row><entry>F(phi,k)</entry><entry><action>incomplete elliptic integral F(phi,k)</action></entry></row> +<row><entry>E(phi,k)</entry><entry><action>incomplete elliptic integral E(phi,k)</action></entry></row> +<row><entry>P(phi,k,n)</entry><entry><action>incomplete elliptic integral P(phi,k,n)</action></entry></row> +<row><entry>D(phi,k,n)</entry><entry><action>incomplete elliptic integral D(phi,k,n)</action></entry></row> +<row><entry>RC(x,y)</entry><entry><action>incomplete elliptic integral RC(x,y)</action></entry></row> +<row><entry>RD(x,y,z)</entry><entry><action>incomplete elliptic integral RD(x,y,z)</action></entry></row> +<row><entry>RF(x,y,z)</entry><entry><action>incomplete elliptic integral RF(x,y,z)</action></entry></row> +<row><entry>RJ(x,y,z)</entry><entry><action>incomplete elliptic integral RJ(x,y,z,p)</action></entry></row> +<row><entry>erf(x)</entry><entry><action>error function erf(x) = 2/√π ∫<subscript>0</subscript><superscript>x</superscript> exp(-t<superscript>2</superscript>) dt</action></entry></row> +<row><entry>erfc(x)</entry><entry><action>complementary error function erfc(x) = 1 - erf(x) = 2/√π ∫<subscript>x</subscript><superscript>∞</superscript> exp(-t<superscript>2</superscript>) dt</action></entry></row> +<row><entry>log_erfc(x)</entry><entry><action>logarithm of the complementary error function log(erfc(x))</action></entry></row> +<row><entry>erf_Z(x)</entry><entry><action>Gaussian probability function Z(x) = (1/(2π)) exp(-x<superscript>2</superscript>/2)</action></entry></row> +<row><entry>erf_Q(x)</entry><entry><action>upper tail of the Gaussian probability function Q(x) = (1/(2π)) ∫<subscript>x</subscript><superscript>∞</superscript> exp(-t<superscript>2</superscript>/2) dt</action></entry></row> +<row><entry>hazard(x)</entry><entry><action>hazard function for the normal distribution</action></entry></row> +<row><entry>exp_mult(x,x)</entry><entry><action>exponentiate x and multiply by the factor y to return the product y exp(x)</action></entry></row> +<row><entry>exprel(x)</entry><entry><action>(exp(x)-1)/x using an algorithm that is accurate for small x</action></entry></row> +<row><entry>exprel2(x)</entry><entry><action>2(exp(x)-1-x)/x<superscript>2</superscript> using an algorithm that is accurate for small x</action></entry></row> +<row><entry>expreln(n,x)</entry><entry><action>n-relative exponential, which is the n-th generalization of the functions `exprel'</action></entry></row> +<row><entry>E1(x)</entry><entry><action>exponential integral E<subscript>1</subscript>(x), E<subscript>1</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t dt</action></entry></row> +<row><entry>E2(x)</entry><entry><action>second-order exponential integral E<subscript>2</subscript>(x), E<subscript>2</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t<superscript>2</superscript> dt</action></entry></row> +<row><entry>En(x)</entry><entry><action>exponential integral E_n(x) of order n, E<subscript>n</subscript>(x) := Re ∫<subscript>1</subscript><superscript>∞</superscript> exp(-xt)/t<superscript>n</superscript> dt)</action></entry></row> +<row><entry>Ei(x)</entry><entry><action>exponential integral E_i(x), Ei(x) := PV(∫<subscript>-x</subscript><superscript>∞</superscript> exp(-t)/t dt)</action></entry></row> +<row><entry>shi(x)</entry><entry><action>Shi(x) = ∫<subscript>0</subscript><superscript>x</superscript> sinh(t)/t dt</action></entry></row> +<row><entry>chi(x)</entry><entry><action>integral Chi(x) := Re[ γ<subscript>E</subscript> + log(x) + ∫<subscript>0</subscript><superscript>x</superscript> (cosh[t]-1)/t dt ]</action></entry></row> +<row><entry>Ei3(x)</entry><entry><action>exponential integral Ei<subscript>3</subscript>(x) = ∫<subscript>0</subscript><superscript>x</superscript> exp(-t<superscript>3</superscript>) dt for x >= 0</action></entry></row> +<row><entry>si(x)</entry><entry><action>Sine integral Si(x) = ∫<subscript>0</subscript><superscript>x</superscript> sin(t)/t dt</action></entry></row> +<row><entry>ci(x)</entry><entry><action>Cosine integral Ci(x) = -∫<subscript>x</subscript><superscript>∞</superscript> cos(t)/t dt for x > 0</action></entry></row> +<row><entry>atanint(x)</entry><entry><action>Arctangent integral AtanInt(x) = ∫<subscript>0</subscript><superscript>x</superscript> arctan(t)/t dt</action></entry></row> +<row><entry>Fm1(x)</entry><entry><action>complete Fermi-Dirac integral with an index of -1, F<subscript>-1</subscript>(x) = e<superscript>x</superscript> / (1 + e<superscript>x</superscript>)</action></entry></row> +<row><entry>F0(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 0, F<subscript>0</subscript>(x) = ln(1 + e<superscript>x</superscript>)</action></entry></row> +<row><entry>F1(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 1, F<subscript>1</subscript>(x) = ∫<subscript>0</subscript><superscript>∞</superscript> (t /(exp(t-x)+1)) dt</action></entry></row> +<row><entry>F2(x)</entry><entry><action>complete Fermi-Dirac integral with an index of 2, F<subscript>2</subscript>(x) = (1/2) ∫<subscript>0</subscript><superscript>∞</superscript> (t<superscript>2</superscript> /(exp(t-x)+1)) dt</action></entry></row> +<row><entry>Fj(j,x)</entry><entry><action>complete Fermi-Dirac integral with an index of j, F<subscript>j</subscript>(x) = (1/Γ(j+1)) ∫<subscript>0</subscript><superscript>∞</superscript> (t<superscript>j</superscript> /(exp(t-x)+1)) dt</action></entry></row> +<row><entry>Fmhalf(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>-1/2</subscript>(x)</action></entry></row> +<row><entry>Fhalf(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>1/2</subscript>(x)</action></entry></row> +<row><entry>F3half(x)</entry><entry><action>complete Fermi-Dirac integral F<subscript>3/2</subscript>(x)</action></entry></row> +<row><entry>Finc0(x,b)</entry><entry><action>incomplete Fermi-Dirac integral with an index of zero, F<subscript>0</subscript>(x,b) = ln(1 + e<superscript>b-x</superscript>) - (b-x)</action></entry></row> +<row><entry>lngamma(x)</entry><entry><action>logarithm of the Gamma function</action></entry></row> +<row><entry>gammastar(x)</entry><entry><action>regulated Gamma Function Γ<superscript>*</superscript>(x) for x > 0</action></entry></row> +<row><entry>gammainv(x)</entry><entry><action>reciprocal of the gamma function, 1/Γ(x) using the real Lanczos method.</action></entry></row> +<row><entry>fact(n)</entry><entry><action>factorial n!</action></entry></row> +<row><entry>doublefact(n)</entry><entry><action>double factorial n!! = n(n-2)(n-4)...</action></entry></row> +<row><entry>lnfact(n)</entry><entry><action>logarithm of the factorial of n, log(n!)</action></entry></row> +<row><entry>lndoublefact(n)</entry><entry><action>logarithm of the double factorial log(n!!)</action></entry></row> +<row><entry>choose(n,m)</entry><entry><action>combinatorial factor `n choose m' = n!/(m!(n-m)!)</action></entry></row> +<row><entry>lnchoose(n,m)</entry><entry><action>logarithm of `n choose m'</action></entry></row> +<row><entry>taylor(n,x)</entry><entry><action>Taylor coefficient x<superscript>n</superscript> / n! for x >= 0, n >= 0</action></entry></row> +<row><entry>poch(a,x)</entry><entry><action>Pochhammer symbol (a)<subscript>x</subscript> := Γ(a + x)/Γ(x)</action></entry></row> +<row><entry>lnpoch(a,x)</entry><entry><action>logarithm of the Pochhammer symbol (a)<subscript>x</subscript> := Γ(a + x)/Γ(x)</action></entry></row> +<row><entry>pochrel(a,x)</entry><entry><action>relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)<subscript>x</subscript> := Γ(a + x)/Γ(a)</action></entry></row> +<row><entry>gammainc(a,x)</entry><entry><action>incomplete Gamma Function Γ(a,x) = ∫<subscript>x</subscript><superscript>∞</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> +<row><entry>gammaincQ(a,x)</entry><entry><action>normalized incomplete Gamma Function P(a,x) = 1/Γ(a) ∫<subscript>x</subscript><superscript>∞</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> +<row><entry>gammaincP(a,x)</entry><entry><action>complementary normalized incomplete Gamma Function P(a,x) = 1/Γ(a) ∫<subscript>0</subscript><superscript>x</superscript> t<superscript>a-1</superscript> exp(-t) dt for a > 0, x >= 0</action></entry></row> +<row><entry>beta(a,b)</entry><entry><action>Beta Function, B(a,b) = Γ(a) Γ(b)/Γ(a+b) for a > 0, b > 0</action></entry></row> +<row><entry>lnbeta(a,b)</entry><entry><action>logarithm of the Beta Function, log(B(a,b)) for a > 0, b > 0</action></entry></row> +<row><entry>betainc(a,b,x)</entry><entry><action>normalize incomplete Beta function B_x(a,b)/B(a,b) for a > 0, b > 0 </action></entry></row> +<row><entry>C1(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>1</subscript>(x)</action></entry></row> +<row><entry>C2(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>2</subscript>(x)</action></entry></row> +<row><entry>C3(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>3</subscript>(x)</action></entry></row> +<row><entry>Cn(n,λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>n</subscript>(x)</action></entry></row> +<row><entry>hyperg_0F1(c,x)</entry><entry><action>hypergeometric function <subscript>0</subscript>F<subscript>1</subscript>(c,x)</action></entry></row> +<row><entry>hyperg_1F1i(m,n,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(m,n,x) = M(m,n,x) for integer parameters m, n</action></entry></row> +<row><entry>hyperg_1F1(a,b,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(a,b,x) = M(a,b,x) for general parameters a,b</action></entry></row> +<row><entry>hyperg_Ui(m,n,x)</entry><entry><action>confluent hypergeometric function U(m,n,x) for integer parameters m,n</action></entry></row> +<row><entry>hyperg_U(a,b,x)</entry><entry><action>confluent hypergeometric function U(a,b,x)</action></entry></row> +<row><entry>hyperg_2F1(a,b,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x)</action></entry></row> +<row><entry>hyperg_2F1c(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) with complex parameters</action></entry></row> +<row><entry>hyperg_2F1r(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x) / Γ(c)</action></entry></row> +<row><entry>hyperg_2F1cr(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) / Γ(c)</action></entry></row> +<row><entry>hyperg_2F0(a,b,x)</entry><entry><action>hypergeometric function <subscript>2</subscript>F<subscript>0</subscript>(a,b,x)</action></entry></row> +<row><entry>L1(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>1</subscript>(x)</action></entry></row> +<row><entry>L2(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>2</subscript>(x)</action></entry></row> +<row><entry>L3(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>3</subscript>(x)</action></entry></row> +<row><entry>W0(x)</entry><entry><action>principal branch of the Lambert W function, W<subscript>0</subscript>(x)</action></entry></row> +<row><entry>Wm1(x)</entry><entry><action>secondary real-valued branch of the Lambert W function, W<subscript>-1</subscript>(x)</action></entry></row> +<row><entry>P1(x)</entry><entry><action>Legendre polynomials P<subscript>1</subscript>(x)</action></entry></row> +<row><entry>P2(x)</entry><entry><action>Legendre polynomials P<subscript>2</subscript>(x)</action></entry></row> +<row><entry>P3(x)</entry><entry><action>Legendre polynomials P<subscript>3</subscript>(x)</action></entry></row> +<row><entry>Pl(l,x)</entry><entry><action>Legendre polynomials P<subscript>l</subscript>(x)</action></entry></row> +<row><entry>Q0(x)</entry><entry><action>Legendre polynomials Q<subscript>0</subscript>(x)</action></entry></row> +<row><entry>Q1(x)</entry><entry><action>Legendre polynomials Q<subscript>1</subscript>(x)</action></entry></row> +<row><entry>Ql(l,x)</entry><entry><action>Legendre polynomials Q<subscript>l</subscript>(x)</action></entry></row> +<row><entry>Plm(l,m,x)</entry><entry><action>associated Legendre polynomial P<subscript>l</subscript><superscript>m</superscript>(x)</action></entry></row> +<row><entry>Pslm(l,m,x)</entry><entry><action>normalized associated Legendre polynomial √{(2l+1)/(4π)} √{(l-m)!/(l+m)!} P<subscript>l</subscript><superscript>m</superscript>(x) suitable for use in spherical harmonics</action></entry></row> +<row><entry>Phalf(λ,x)</entry><entry><action>irregular Spherical Conical Function P<superscript>1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pmhalf(λ,x)</entry><entry><action>regular Spherical Conical Function P<superscript>-1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pc0(λ,x)</entry><entry><action>conical function P<superscript>0</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pc1(λ,x)</entry><entry><action>conical function P<superscript>1</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Psr(l,λ,x)</entry><entry><action>Regular Spherical Conical Function P<superscript>-1/2-l</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, l >= -1</action></entry></row> +<row><entry>Pcr(l,λ,x)</entry><entry><action>Regular Cylindrical Conical Function P<superscript>-m</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, m >= -1</action></entry></row> +<row><entry>H3d0(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>0</subscript>(λ,,η) := sin(λ η)/(λ sinh(η)) for η >= 0</action></entry></row> +<row><entry>H3d1(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>1</subscript>(λ,η) := 1/√{λ<superscript>2</superscript> + 1} sin(λ η)/(λ sinh(η)) (coth(η) - λ cot(λ η)) for η >= 0</action></entry></row> +<row><entry>H3d(l,λ,η)</entry><entry><action>L'th radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space eta >= 0, l >= 0</action></entry></row> +<row><entry>logabs(x)</entry><entry><action>logarithm of the magnitude of X, log(|x|)</action></entry></row> +<row><entry>logp(x)</entry><entry><action>log(1 + x) for x > -1 using an algorithm that is accurate for small x</action></entry></row> +<row><entry>logm(x)</entry><entry><action>log(1 + x) - x for x > -1 using an algorithm that is accurate for small x</action></entry></row> +<row><entry>psiint(n)</entry><entry><action>digamma function ψ(n) for positive integer n</action></entry></row> +<row><entry>psi(x)</entry><entry><action>digamma function ψ(n) for general x</action></entry></row> +<row><entry>psi1piy(y)</entry><entry><action>real part of the digamma function on the line 1+i y, Re[ψ(1 + i y)]</action></entry></row> +<row><entry>psi1int(n)</entry><entry><action>Trigamma function ψ'(n) for positive integer n</action></entry></row> +<row><entry>psi1(n)</entry><entry><action>Trigamma function ψ'(x) for general x</action></entry></row> +<row><entry>psin(m,x)</entry><entry><action>polygamma function ψ<superscript>(m)</superscript>(x) for m >= 0, x > 0</action></entry></row> +<row><entry>synchrotron1(x)</entry><entry><action>first synchrotron function x ∫<subscript>x</subscript><superscript>∞</superscript> K<subscript>5/3</subscript>(t) dt for x >= 0</action></entry></row> +<row><entry>synchrotron2(x)</entry><entry><action>second synchrotron function x K<subscript>2/3</subscript>(x) for x >= 0</action></entry></row> +<row><entry>J2(x)</entry><entry><action>transport function J(2,x)</action></entry></row> +<row><entry>J3(x)</entry><entry><action>transport function J(3,x)</action></entry></row> +<row><entry>J4(x)</entry><entry><action>transport function J(4,x)</action></entry></row> +<row><entry>J5(x)</entry><entry><action>transport function J(5,x)</action></entry></row> +<row><entry>sinc(x)</entry><entry><action>sinc(x) = sin(π x) / (π x)</action></entry></row> +<row><entry>logsinh(x)</entry><entry><action>log(sinh(x)) for x > 0</action></entry></row> +<row><entry>logcosh(x)</entry><entry><action>log(cosh(x))</action></entry></row> +<row><entry>anglesymm(α)</entry><entry><action>force the angle α to lie in the range (-π,π]</action></entry></row> +<row><entry>anglepos(α)</entry><entry><action>force the angle α to lie in the range (0,2π]</action></entry></row> +<row><entry>zetaint(n)</entry><entry><action>Riemann zeta function ζ(n) for integer n</action></entry></row> +<row><entry>zeta(s)</entry><entry><action>Riemann zeta function ζ(s) for arbitrary s</action></entry></row> +<row><entry>zetam1int(n)</entry><entry><action>Riemann ζ function minus 1 for integer n</action></entry></row> +<row><entry>zetam1(s)</entry><entry><action>Riemann ζ function minus 1</action></entry></row> +<row><entry>zetaintm1(s)</entry><entry><action>Riemann ζ function for integer n minus 1</action></entry></row> +<row><entry>hzeta(s,q)</entry><entry><action>Hurwitz zeta function ζ(s,q) for s > 1, q > 0</action></entry></row> +<row><entry>etaint(n)</entry><entry><action>eta function η(n) for integer n</action></entry></row> +<row><entry>eta(s)</entry><entry><action>eta function η(s) for arbitrary s</action></entry></row> +<row><entry>gsl_log1p(x)</entry><entry><action>log(1+x)</action></entry></row> +<row><entry>gsl_expm1(x)</entry><entry><action>exp(x)-1</action></entry></row> +<row><entry>gsl_hypot(x,y)</entry><entry><action>√{x<superscript>2</superscript> + y<superscript>2</superscript>}</action></entry></row> +<row><entry>gsl_acosh(x)</entry><entry><action>arccosh(x)</action></entry></row> +<row><entry>gsl_asinh(x)</entry><entry><action>arcsinh(x)</action></entry></row> +<row><entry>gsl_atanh(x)</entry><entry><action>arctanh(x)</action></entry></row> +</tbody> +</tgroup> +</informaltable> +</sect1> +<sect1 id="parser-ran-gsl"> +<title>Random number distributions</title> <para> -Because there are a lot things to do, developers need every help you can give. Any contribution like wishes, corrections, -patches, bug reports or screen shots is welcome. +For more information about the functions see the documentation of GSL. </para> +<informaltable pgwide="1"><tgroup cols="2"> -<para> -Documentation copyright © 2007-2015 Stefan Gerlach -<email>[email protected]</email> +<thead><row><entry>Function</entry><entry>Description</entry></row></thead> -Documentation copyright © 2008-2015 Alexander Semke -<email>[email protected]</email> +<tbody> -Documentation copyright © 2014 Yuri Chornoivan -<email>[email protected]</email> -</para> +<row><entry>gaussian(x,σ)</entry><entry><action>probability density p(x) for a Gaussian distribution with standard deviation σ</action></entry></row> +<row><entry>ugaussian(x)</entry><entry><action>unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1</action></entry></row> +<row><entry>gaussianP(x,σ)</entry><entry><action>cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ</action></entry></row> +<row><entry>gaussianQ(x,σ)</entry><entry><action>cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ</action></entry></row> +<row><entry>gaussianPinv(P,σ)</entry><entry><action>inverse cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ</action></entry></row> +<row><entry>gaussianQinv(Q,σ)</entry><entry><action>inverse cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ</action></entry></row> +<row><entry>ugaussianP(x)</entry><entry><action>cumulative distribution function P(x) for the unit Gaussian distribution</action></entry></row> +<row><entry>ugaussianQ(x)</entry><entry><action>cumulative distribution function Q(x) for the unit Gaussian distribution</action></entry></row> +<row><entry>ugaussianPinv(P)</entry><entry><action>inverse cumulative distribution function P(x) for the unit Gaussian distribution</action></entry></row> +<row><entry>ugaussianQinv(Q)</entry><entry><action>inverse cumulative distribution function Q(x) for the unit Gaussian distribution</action></entry></row> +<row><entry>gaussiantail(x,a,σ)</entry><entry><action>probability density p(x) for a Gaussian tail distribution with standard deviation σ and lower limit a</action></entry></row> +<row><entry>ugaussiantail(x,a)</entry><entry><action>tail of a unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1</action></entry></row> +<row><entry>gaussianbi(x,y,σ<subscript>x</subscript>,σ<subscript>y</subscript>,ρ)</entry><entry><action>probability density p(x,y) for a bivariate gaussian distribution + with standard deviations σ<subscript>x</subscript>, σ<subscript>y</subscript> and correlation coefficient ρ</action></entry></row> +<row><entry>exponential(x,μ)</entry><entry><action>probability density p(x) for an exponential distribution with mean μ</action></entry></row> +<row><entry>exponentialP(x,μ)</entry><entry><action>cumulative distribution function P(x) for an exponential distribution with mean μ</action></entry></row> +<row><entry>exponentialQ(x,μ)</entry><entry><action>cumulative distribution function Q(x) for an exponential distribution with mean μ</action></entry></row> +<row><entry>exponentialPinv(P,μ)</entry><entry><action>inverse cumulative distribution function P(x) for an exponential distribution with mean μ</action></entry></row> +<row><entry>exponentialQinv(Q,μ)</entry><entry><action>inverse cumulative distribution function Q(x) for an exponential distribution with mean μ</action></entry></row> +<row><entry>laplace(x,a)</entry><entry><action>probability density p(x) for a Laplace distribution with width a</action></entry></row> +<row><entry>laplaceP(x,a)</entry><entry><action>cumulative distribution function P(x) for a Laplace distribution with width a</action></entry></row> +<row><entry>laplaceQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a Laplace distribution with width a</action></entry></row> +<row><entry>laplacePinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for an Laplace distribution with width a</action></entry></row> +<row><entry>laplaceQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for an Laplace distribution with width a</action></entry></row> +<row><entry>exppow(x,a,b)</entry><entry><action>probability density p(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> +<row><entry>exppowP(x,a,b)</entry><entry><action>cumulative probability density P(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> +<row><entry>exppowQ(x,a,b)</entry><entry><action>cumulative probability density Q(x) for an exponential power distribution with scale parameter a and exponent b</action></entry></row> +<row><entry>cauchy(x,a)</entry><entry><action>probability density p(x) for a Cauchy (Lorentz) distribution with scale parameter a</action></entry></row> +<row><entry>cauchyP(x,a)</entry><entry><action>cumulative distribution function P(x) for a Cauchy distribution with scale parameter a</action></entry></row> +<row><entry>cauchyQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a</action></entry></row> +<row><entry>cauchyPinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for a Cauchy distribution with scale parameter a</action></entry></row> +<row><entry>cauchyQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a</action></entry></row> +<row><entry>rayleigh(x,σ)</entry><entry><action>probability density p(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> +<row><entry>rayleighP(x,σ)</entry><entry><action>cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> +<row><entry>rayleighQ(x,σ)</entry><entry><action>cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> +<row><entry>rayleighPinv(P,σ)</entry><entry><action>inverse cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> +<row><entry>rayleighQinv(Q,σ)</entry><entry><action>inverse cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ</action></entry></row> +<row><entry>rayleigh_tail(x,a,σ)</entry><entry><action>probability density p(x) for a Rayleigh tail distribution with scale parameter σ and lower limit a</action></entry></row> +<row><entry>landau(x)</entry><entry><action>probability density p(x) for the Landau distribution</action></entry></row> +<row><entry>gammapdf(x,a,b)</entry><entry><action>probability density p(x) for a gamma distribution with parameters a and b</action></entry></row> +<row><entry>gammaP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a gamma distribution with parameters a and b</action></entry></row> +<row><entry>gammaQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a gamma distribution with parameters a and b</action></entry></row> +<row><entry>gammaPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a gamma distribution with parameters a and b</action></entry></row> +<row><entry>gammaQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a gamma distribution with parameters a and b</action></entry></row> +<row><entry>flat(x,a,b)</entry><entry><action>probability density p(x) for a uniform distribution from a to b</action></entry></row> +<row><entry>flatP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a uniform distribution from a to b</action></entry></row> +<row><entry>flatQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a uniform distribution from a to b</action></entry></row> +<row><entry>flatPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a uniform distribution from a to b</action></entry></row> +<row><entry>flatQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a uniform distribution from a to b</action></entry></row> +<row><entry>lognormal(x,ζ,σ)</entry><entry><action>probability density p(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> +<row><entry>lognormalP(x,ζ,σ)</entry><entry><action>cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> +<row><entry>lognormalQ(x,ζ,σ)</entry><entry><action>cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> +<row><entry>lognormalPinv(P,ζ,σ)</entry><entry><action>inverse cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> +<row><entry>lognormalQinv(Q,ζ,σ)</entry><entry><action>inverse cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ</action></entry></row> +<row><entry>chisq(x,ν)</entry><entry><action>probability density p(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> +<row><entry>chisqP(x,ν)</entry><entry><action>cumulative distribution function P(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> +<row><entry>chisqQ(x,ν)</entry><entry><action>cumulative distribution function Q(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> +<row><entry>chisqPinv(P,ν)</entry><entry><action>inverse cumulative distribution function P(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> +<row><entry>chisqQinv(Q,ν)</entry><entry><action>inverse cumulative distribution function Q(x) for a χ<superscript>2</superscript> distribution with ν degrees of freedom</action></entry></row> +<row><entry>fdist(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>probability density p(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> +<row><entry>fdistP(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>cumulative distribution function P(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> +<row><entry>fdistQ(x,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>cumulative distribution function Q(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> +<row><entry>fdistPinv(P,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>inverse cumulative distribution function P(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> +<row><entry>fdistQinv(Q,ν<subscript>1</subscript>,ν<subscript>2</subscript>)</entry><entry><action>inverse cumulative distribution function Q(x) for an F-distribution with ν<subscript>1</subscript> and ν<subscript>2</subscript> degrees of freedom</action></entry></row> +<row><entry>tdist(x,ν)</entry><entry><action>probability density p(x) for a t-distribution with ν degrees of freedom</action></entry></row> +<row><entry>tdistP(x,ν)</entry><entry><action>cumulative distribution function P(x) for a t-distribution with ν degrees of freedom</action></entry></row> +<row><entry>tdistQ(x,ν)</entry><entry><action>cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom</action></entry></row> +<row><entry>tdistPinv(P,ν)</entry><entry><action>inverse cumulative distribution function P(x) for a t-distribution with ν degrees of freedom</action></entry></row> +<row><entry>tdistQinv(Q,ν)</entry><entry><action>inverse cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom</action></entry></row> +<row><entry>betapdf(x,a,b)</entry><entry><action>probability density p(x) for a beta distribution with parameters a and b</action></entry></row> +<row><entry>betaP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a beta distribution with parameters a and b</action></entry></row> +<row><entry>betaQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a beta distribution with parameters a and b</action></entry></row> +<row><entry>betaPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a beta distribution with parameters a and b</action></entry></row> +<row><entry>betaQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a beta distribution with parameters a and b</action></entry></row> +<row><entry>logistic(x,a)</entry><entry><action>probability density p(x) for a logistic distribution with scale parameter a</action></entry></row> +<row><entry>logisticP(x,a)</entry><entry><action>cumulative distribution function P(x) for a logistic distribution with scale parameter a</action></entry></row> +<row><entry>logisticQ(x,a)</entry><entry><action>cumulative distribution function Q(x) for a logistic distribution with scale parameter a</action></entry></row> +<row><entry>logisticPinv(P,a)</entry><entry><action>inverse cumulative distribution function P(x) for a logistic distribution with scale parameter a</action></entry></row> +<row><entry>logisticQinv(Q,a)</entry><entry><action>inverse cumulative distribution function Q(x) for a logistic distribution with scale parameter a</action></entry></row> +<row><entry>pareto(x,a,b)</entry><entry><action>probability density p(x) for a Pareto distribution with exponent a and scale b</action></entry></row> +<row><entry>paretoP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b</action></entry></row> +<row><entry>paretoQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b</action></entry></row> +<row><entry>paretoPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b</action></entry></row> +<row><entry>paretoQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b</action></entry></row> +<row><entry>weibull(x,a,b)</entry><entry><action>probability density p(x) for a Weibull distribution with scale a and exponent b</action></entry></row> +<row><entry>weibullP(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b</action></entry></row> +<row><entry>weibullQ(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b</action></entry></row> +<row><entry>weibullPinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b</action></entry></row> +<row><entry>weibullQinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b</action></entry></row> +<row><entry>gumbel1(x,a,b)</entry><entry><action>probability density p(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel1P(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel1Q(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel1Pinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel1Qinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel2(x,a,b)</entry><entry><action>probability density p(x) at X for a Type-2 Gumbel distribution with parameters A and B</action></entry></row> +<row><entry>gumbel2P(x,a,b)</entry><entry><action>cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel2Q(x,a,b)</entry><entry><action>cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel2Pinv(P,a,b)</entry><entry><action>inverse cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>gumbel2Qinv(Q,a,b)</entry><entry><action>inverse cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b</action></entry></row> +<row><entry>poisson(k,μ)</entry><entry><action>probability p(k) of obtaining k from a Poisson distribution with mean μ</action></entry></row> +<row><entry>poissonP(k,μ)</entry><entry><action>cumulative distribution functions P(k) for a Poisson distribution with mean μ</action></entry></row> +<row><entry>poissonQ(k,μ)</entry><entry><action>cumulative distribution functions Q(k) for a Poisson distribution with mean μ</action></entry></row> +<row><entry>bernoulli(k,p)</entry><entry><action>probability p(k) of obtaining k from a Bernoulli distribution with probability parameter p</action></entry></row> +<row><entry>binomial(k,p,n)</entry><entry><action>probability p(k) of obtaining p from a binomial distribution with parameters p and n</action></entry></row> +<row><entry>binomialP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a binomial distribution with parameters p and n</action></entry></row> +<row><entry>binomialQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a binomial distribution with parameters p and n</action></entry></row> +<row><entry>nbinomial(k,p,n)</entry><entry><action>probability p(k) of obtaining k from a negative binomial distribution with parameters p and n</action></entry></row> +<row><entry>nbinomialP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a negative binomial distribution with parameters p and n</action></entry></row> +<row><entry>nbinomialQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a negative binomial distribution with parameters p and n</action></entry></row> +<row><entry>pascal(k,p,n)</entry><entry><action>probability p(k) of obtaining k from a Pascal distribution with parameters p and n</action></entry></row> +<row><entry>pascalP(k,p,n)</entry><entry><action>cumulative distribution functions P(k) for a Pascal distribution with parameters p and n</action></entry></row> +<row><entry>pascalQ(k,p,n)</entry><entry><action>cumulative distribution functions Q(k) for a Pascal distribution with parameters p and n</action></entry></row> +<row><entry>geometric(k,p)</entry><entry><action>probability p(k) of obtaining k from a geometric distribution with probability parameter p</action></entry></row> +<row><entry>geometricP(k,p)</entry><entry><action>cumulative distribution functions P(k) for a geometric distribution with parameter p</action></entry></row> +<row><entry>geometricQ(k,p)</entry><entry><action>cumulative distribution functions Q(k) for a geometric distribution with parameter p</action></entry></row> +<row><entry>hypergeometric(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>probability p(k) of obtaining k from a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> +<row><entry>hypergeometricP(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>cumulative distribution function P(k) for a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> +<row><entry>hypergeometricQ(k,n<subscript>1</subscript>,n<subscript>2</subscript>,t)</entry><entry><action>cumulative distribution function Q(k) for a hypergeometric distribution with parameters n<subscript>1</subscript>, n<subscript>2</subscript>, t</action></entry></row> +<row><entry>logarithmic(k,p)</entry><entry><action>probability p(k) of obtaining K from a logarithmic distribution with probability parameter p</action></entry></row> +</tbody> +</tgroup> +</informaltable> +</sect1> -<!-- TRANS:CREDIT_FOR_TRANSLATORS --> +<sect1 id="parser-const"> +<title>Constants</title> -&underFDL; -&underGPL; +<informaltable pgwide="1"><tgroup cols="2"> -</chapter> +<thead><row><entry>Constant</entry><entry>Description</entry></row></thead> -<appendix id="installation"> -<title>Installation</title> +<tbody> -<sect1 id="getting-labplot"> -<title>How to Obtain &LabPlot;</title> +<row><entry>e</entry><entry><action>The base of natural logarithms</action></entry></row> +<row><entry>pi</entry><entry><action>π</action></entry></row> -<para> -&LabPlot; can be found on its homepage at sourceforge.net: -<ulink url="http://labplot.sf.net";>http://labplot.sf.net</ulink>. -There is an overview about all available packages at -<ulink url="http://labplot.wiki.sourceforge.net/Download";>http://labplot.wiki.sourceforge.net/Download</ulink>. -bug-fixed packages are released regular and can be found there too. -</para> +</tbody></tgroup></informaltable> </sect1> -<sect1 id="requirements"> -<title>Requirements</title> - +<sect1 id="parser-const-gsl"> +<title>GSL constants</title> <para> -In order to successfully use &LabPlot;, you need at least a standard &Qt; 5 and &kde; KF5 installation, the &GNU; scientific library (GSL), &cantor; libcantor library. -</para> - -<!-- <para> -Optional &LabPlot; uses the following programs/libraries when available: +For more information about this constants see the documentation of GSL. </para> +<informaltable pgwide="1"><tgroup cols="2"> -<itemizedlist> -<listitem><para> -&GNU; scientific library (GSL) : used for special functions in the parser and most of the analysis functions. -</para></listitem> -</itemizedlist> ---> +<thead><row><entry>Constant</entry><entry>Description</entry></row></thead> -</sect1> +<tbody> -<sect1 id="compilation"> -<title>Compilation and Installation</title> +<row><entry>c</entry><entry><action> The speed of light in vacuum</action></entry></row> +<row><entry>mu0</entry><entry><action>The permeability of free space</action></entry></row> +<row><entry>e0</entry><entry><action>The permittivity of free space</action></entry></row> +<row><entry>h</entry><entry><action>The Planck constant h</action></entry></row> +<row><entry>hbar</entry><entry><action>The reduced Planck constant ℏ</action></entry></row> +<row><entry>na</entry><entry><action>Avogadro's number</action></entry></row> +<row><entry>f</entry><entry><action>The molar charge of 1 Faraday</action></entry></row> +<row><entry>k</entry><entry><action>The Boltzmann constant</action></entry></row> +<row><entry>r0</entry><entry><action>The molar gas constant</action></entry></row> +<row><entry>v0</entry><entry><action>The standard gas volume</action></entry></row> +<row><entry>sigma</entry><entry><action>The Stefan–Boltzmann constant</action></entry></row> +<row><entry>gauss</entry><entry><action>The magnetic field of 1 Gauss</action></entry></row> +<row><entry>au</entry><entry><action>The length of 1 astronomical unit (mean earth-sun distance)</action></entry></row> +<row><entry>G</entry><entry><action>The gravitational constant</action></entry></row> +<row><entry>ly</entry><entry><action>The distance of 1 light-year</action></entry></row> +<row><entry>pc</entry><entry><action>The distance of 1 parsec</action></entry></row> +<row><entry>gg</entry><entry><action>The standard gravitational acceleration on Earth</action></entry></row> +<row><entry>ms</entry><entry><action>The mass of the Sun</action></entry></row> +<row><entry>ee</entry><entry><action>The charge of the electron</action></entry></row> +<row><entry>eV</entry><entry><action>The energy of 1 electron volt</action></entry></row> +<row><entry>amu</entry><entry><action>The unified atomic mass</action></entry></row> +<row><entry>me</entry><entry><action>The mass of the electron</action></entry></row> +<row><entry>mmu</entry><entry><action>The mass of the muon</action></entry></row> +<row><entry>mp</entry><entry><action>The mass of the proton</action></entry></row> +<row><entry>mn</entry><entry><action>The mass of the neutron</action></entry></row> +<row><entry>alpha</entry><entry><action>The electromagnetic fine structure constant</action></entry></row> +<row><entry>ry</entry><entry><action>The Rydberg constant</action></entry></row> +<row><entry>a0</entry><entry><action>The Bohr radius</action></entry></row> +<row><entry>a</entry><entry><action>The length of 1 angstrom</action></entry></row> +<row><entry>barn</entry><entry><action> The area of 1 barn</action></entry></row> +<row><entry>muB</entry><entry><action>The Bohr Magneton</action></entry></row> +<row><entry>mun</entry><entry><action>The Nuclear Magneton</action></entry></row> +<row><entry>mue</entry><entry><action>The magnetic moment of the electron</action></entry></row> +<row><entry>mup</entry><entry><action>The magnetic moment of the proton</action></entry></row> +<row><entry>sigmaT</entry><entry><action>The Thomson cross section for an electron</action></entry></row> +<row><entry>pD</entry><entry><action>The debye</action></entry></row> +<row><entry>min</entry><entry><action>The number of seconds in 1 minute</action></entry></row> +<row><entry>h</entry><entry><action>The number of seconds in 1 hour</action></entry></row> +<row><entry>d</entry><entry><action> The number of seconds in 1 day</action></entry></row> +<row><entry>week</entry><entry><action>The number of seconds in 1 week</action></entry></row> +<row><entry>in</entry><entry><action>The length of 1 inch</action></entry></row> +<row><entry>ft</entry><entry><action>The length of 1 foot</action></entry></row> +<row><entry>yard</entry><entry><action>The length of 1 yard</action></entry></row> +<row><entry>mil</entry><entry><action>The length of 1 mil (1/1000th of an inch)</action></entry></row> +<row><entry>v_km_per_h</entry><entry><action>The speed of 1 kilometer per hour</action></entry></row> +<row><entry>v_mile_per_h</entry><entry><action>The speed of 1 mile per hour</action></entry></row> +<row><entry>nmile</entry><entry><action>The length of 1 nautical mile</action></entry></row> +<row><entry>fathom</entry><entry><action>The length of 1 fathom</action></entry></row> +<row><entry>knot</entry><entry><action>The speed of 1 knot</action></entry></row> +<row><entry>pt</entry><entry><action> The length of 1 printer's point (1/72 inch)</action></entry></row> +<row><entry>texpt</entry><entry><action>The length of 1 TeX point (1/72.27 inch)</action></entry></row> +<row><entry>micron</entry><entry><action>The length of 1 micrometre</action></entry></row> +<row><entry>hectare</entry><entry><action>The area of 1 hectare</action></entry></row> +<row><entry>acre</entry><entry><action>The area of 1 acre</action></entry></row> +<row><entry>liter</entry><entry><action>The volume of 1 liter</action></entry></row> +<row><entry>us_gallon</entry><entry><action>The volume of 1 US gallon</action></entry></row> +<row><entry>can_gallon</entry><entry><action>The volume of 1 Canadian gallon</action></entry></row> +<row><entry>uk_gallon</entry><entry><action>The volume of 1 UK gallon</action></entry></row> +<row><entry>quart</entry><entry><action>The volume of 1 quart</action></entry></row> +<row><entry>pint</entry><entry><action>The volume of 1 pint</action></entry></row> +<row><entry>pound</entry><entry><action>The mass of 1 pound</action></entry></row> +<row><entry>ounce</entry><entry><action>The mass of 1 ounce</action></entry></row> +<row><entry>ton</entry><entry><action>The mass of 1 ton</action></entry></row> +<row><entry>mton</entry><entry><action>The mass of 1 metric ton (1000 kg)</action></entry></row> +<row><entry>uk_ton</entry><entry><action>The mass of 1 UK ton</action></entry></row> +<row><entry>troy_ounce</entry><entry><action>The mass of 1 troy ounce</action></entry></row> +<row><entry>carat</entry><entry><action>The mass of 1 carat</action></entry></row> +<row><entry>gram_force</entry><entry><action>The force of 1 gram weight</action></entry></row> +<row><entry>pound_force</entry><entry><action>The force of 1 pound weight</action></entry></row> +<row><entry>kilepound_force</entry><entry><action>The force of 1 kilopound weight</action></entry></row> +<row><entry>poundal</entry><entry><action>The force of 1 poundal</action></entry></row> +<row><entry>cal</entry><entry><action>The energy of 1 calorie</action></entry></row> +<row><entry>btu</entry><entry><action>The energy of 1 British Thermal Unit</action></entry></row> +<row><entry>therm</entry><entry><action>The energy of 1 Therm</action></entry></row> +<row><entry>hp</entry><entry><action>The power of 1 horsepower</action></entry></row> +<row><entry>bar</entry><entry><action>The pressure of 1 bar</action></entry></row> +<row><entry>atm</entry><entry><action>The pressure of 1 standard atmosphere</action></entry></row> +<row><entry>torr</entry><entry><action>The pressure of 1 torr</action></entry></row> +<row><entry>mhg</entry><entry><action>The pressure of 1 meter of mercury</action></entry></row> +<row><entry>inhg</entry><entry><action>The pressure of 1 inch of mercury</action></entry></row> +<row><entry>inh2o</entry><entry><action>The pressure of 1 inch of water</action></entry></row> +<row><entry>psi</entry><entry><action>The pressure of 1 pound per square inch</action></entry></row> +<row><entry>poise</entry><entry><action>The dynamic viscosity of 1 poise</action></entry></row> +<row><entry>stokes</entry><entry><action>The kinematic viscosity of 1 stokes</action></entry></row> +<row><entry>stilb</entry><entry><action>The luminance of 1 stilb</action></entry></row> +<row><entry>lumen</entry><entry><action>The luminous flux of 1 lumen</action></entry></row> +<row><entry>lux</entry><entry><action>The illuminance of 1 lux</action></entry></row> +<row><entry>phot</entry><entry><action>The illuminance of 1 phot</action></entry></row> +<row><entry>ftcandle</entry><entry><action>The illuminance of 1 footcandle</action></entry></row> +<row><entry>lambert</entry><entry><action>The luminance of 1 lambert</action></entry></row> +<row><entry>ftlambert</entry><entry><action>The luminance of 1 footlambert</action></entry></row> +<row><entry>curie</entry><entry><action>The activity of 1 curie</action></entry></row> +<row><entry>roentgen</entry><entry><action>The exposure of 1 roentgen</action></entry></row> +<row><entry>rad</entry><entry><action>The absorbed dose of 1 rad</action></entry></row> +<row><entry>N</entry><entry><action>The force of 1 newton</action></entry></row> +<row><entry>dyne</entry><entry><action>The force of 1 dyne</action></entry></row> +<row><entry>J</entry><entry><action>The energy of 1 joule</action></entry></row> +<row><entry>erg</entry><entry><action>The energy of 1 erg</action></entry></row> -&install.compile.documentation; +</tbody></tgroup></informaltable> </sect1>
