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

Subject: Re: [boost] GSoC Hypergeometric functions (Pratyaksh Sharma)
From: John Maddock (boost.regex_at_[hidden])
Date: 2014-02-07 05:17:02

> I know it's not best idea now,
> but I just tried to implement Taylor series,
> because I don't have the book right now.
> If it is interesting, please look at
> https://github.com/AntonBikineev/math/blob/hypergeometric/include/
> boost/math/special_functions/detail/hypergeometric_pfq_series.hpp
>
> Also I have some ideas about reducing division operators in sum
> and thereby reducing rounding errors.

Nice.

I guess the complicated part of implementing these functions is figuring 
out how to divide up the input domain:

1) When these series can safely be used.
2) When the result is a domain error.
3) When the result is necessarily infinity (series diverges to +INF).
4) When you can use recurrence relations and other identities to move 
closer to (1), and if those relations are stable.  If the recursion is 
unstable then can something like Millers algorithm be used.

Cheers, John.