Hypergeometric functions

marcobonici
Sat, 26 Jun 2021 23:53:40 +0000
Numerics

Hello,
I need to evaluate the Gauss Hypergeometric functions _2F_1(a,b;c;z). Here are some specifications for the arguments of this function

a has compex values. The real part is \sim2 (and is strictly positive), while the complex part ranges from 0 to \sim500

b has compex values. The real part ranges from 10 to \sim5000, while the complex part ranges from 0 to \sim500

c is a real number, which ranges from 10 to 5000

z is a real number, which ranges from 0 to 1.

Which packages should I consider to evaluate _2F_1, given the previous requirements? I have found some existing packages, such as HypergeometricFunctions.jl or Nemo.jl, but I don’t know which one is the most stable/efficient given my requirements. I could also consider to call the mpmath module.
I also add that I value stability and precision, rather then speed. I could evaluate the hypergeometric functions for a fixed grid of a, b, c and z and then I could store the output.

If requested, I can give more details on the numerical integrals I am trying to solve.

Thank you for your help,
Marco

7 posts - 6 participants