Doug Stewart wrote: > [EMAIL PROTECTED] wrote: >> I have been concentrating on Axiom's numerical capabilities. The last >> patch is the beginnings of regression tests against >> Abramowitz and Stegun (1985) and Zwillinger's CRC Standard (2003). >> I've also created firefox hyperdoc pages for the gamma function >> standard from the new DLMF. I plan to fill these pages out with >> Spad code and test cases as time permits. >> >> I'm a member of the Numerical Mathematics Consortium >> (http://www.nmconsortium.org).A recently published draft >> standard, which I'm reviewing, is available at: >> <http://www.nmconsortium.org/docs/NMC_Technical_Specification%20(9-24-2007).pdf> >> >> >> The A&S handbook lists polynomial coefficients for approximation of E1, >> the exponential integral. Does anyone know how these coefficients were >> derived? Is it a chebyshev polynomial? I want to dynamically compute >> these coefficients to the required precision. >> >> Tim >> >> >> _______________________________________________ >> Axiom-developer mailing list >> [email protected] >> http://lists.nongnu.org/mailman/listinfo/axiom-developer >> >> > > > The exponential integral can be written as a special case of the > incomplete gamma function > <http://en.wikipedia.org/wiki/Incomplete_gamma_function>: > > {\rm E}_n(x) =x^{n-1}\Gamma(1-n,x).\, > > The exponential integral may also be generalized to > > E_n(x) = \int_1^\infty \frac{e^{-xt}}{t^n}\, dt > > > this is from > > http://en.wikipedia.org/wiki/Exponential_integral > > > _______________________________________________ > Axiom-developer mailing list > [email protected] > http://lists.nongnu.org/mailman/listinfo/axiom-developer >
P.S.: Another classic from those days was _Approximations for Digital Computers_ by Cecil Hastings. That's on my list of collectibles to pick up. :) _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
