It's believed that such functions are best computed/approximated as continued fractions:
-- http://people.math.sfu.ca/~cbm/aands/page_263.htm FriCAS can do this nicely ;-) >> Gamma.input )r Gamma CF==>Complex Float F(1,a)==1$CF F(n,a)== if even? n then (n/2-a::CF) else (n-1)/2 G(n,x)== if even? n then 1$CF else x::CF sF(a)==[F(n,a) for n in 1..] sG(x)==[G(n,x) for n in 1..] GAMMA(a,x,k)== A:=sF(a)@Stream CF B:=sG(x)@Stream CF g:=continuedFraction(0,A,B) app:=approximants(g) x^a*exp(-x)*app.k -- k: k'th approximation GAMMA(1.0,2.0,100) GAMMA(3.0,5.5,100) GAMMA(3.8,2.4,100) GAMMA(10,12.123,100) GAMMA(5,2::CF,100) -- Check here https://www.danielsoper.com/statcalc/calculator.aspx?id=23 On 18.06.2018 11:30, 'Nasser M. Abbasi' via FriCAS - computer algebra system wrote: > I gave up. > > How can I persuade Fricas to please print a _numerical_ value for say > Gamma[2,3] > ? What is the magic trick? > > in Mathematica, I just add "N" > > In[33]:= N[Gamma[5,2]] > Out[33]= 22.7363 > > I tried > > (16) -> Gamma(5.0,2.0) > (16) Gamma(5.0,2.0) > Type: Expression(Float) > > and > > Gamma(5.0,2.0)::Float > Cannot convert the value from type Expression(Float) to Float . > > and > > eval(Gamma(5.0,2.0)) > (17) Gamma(5.0,2.0) > Type: Expression(Float) > > This is so frustrating. It works on the one argument Gamma > > (18) -> Gamma(5.0) > (18) 23.9999999999_9999999999_99998 > Type: Float > > But not on the 2 argument Gamma > )display op Gamma > > [2] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) > if D2 has Join(COMPAR,INTDOM) and D1 has FS(D2) > > Thank you > --Nasser > > > > > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email > to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/fricas-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
