Re: [boost] GSoC Hypergeometric functions (Pratyaksh Sharma)

Subject: Re: [boost] GSoC Hypergeometric functions (Pratyaksh Sharma)
From: Christopher Kormanyos (e_float_at_[hidden])
Date: 2014-02-03 15:35:41

You could start by trying to compile and work with the detailed
sample code provided in the link on the GSoC project page.

> Just to start the discussion: Does everyone agree that a variety of methods
> need to employed for calculating the functions for different ranges of
> parameters?

Absolutely. We need various methods for various parameter ranges
and also for different precision ranges.

> Taylor series methods for smaller values of |a| and |z|.

Yes, whereby it can be challenging deciding on the range of
convergence.

> Any other ideas?

I like your idea of Gauss-Jacobi quadrature methods.

There is also a *grand new* example featuring generation
of Gauss-Laguerre coefficients for multiple-precision.

https://github.com/boostorg/multiprecision/blob/develop/example/gauss_laguerre_quadrature.cpp

In this project, we will be investigating a variety of calculational
methods including Chebyshev polynomial expansion, rational
approximation, Pade approximation, and perhaps others.

There are also some cool expansions for some hypergeometric
functions in series of Bessel functions.
Best regards, Chris.