Re: [Help-gsl] complex numbers and zeta function

[Ruben Henner Zilibowitz]

Ok I've implemented a zeta function and a gamma function that seem to  
work reasonably well for complex arguments.
Should I post the source file to this mailing list?

I'd like to have a polygamma function that worked for complex  
arguments too, but so far I haven't found any good references on how  
best to implement it.

Ruben

On 17/06/2008, at 7:08 AM, Jordi Gutiérrez Hermoso wrote:

> On 16/06/2008, Ruben Henner Zilibowitz <address@hidden>  
> wrote:
> > Has there been any thought given to implementations of the zeta  
> > function and
> > eta function for complex numbers, instead of just for reals?
>
> I don't know if any thought has been given to it until now, but you're
> right that it doesn't seem to be implemented. I looked around, and I
> saw it in Pari ($PARI_SOURCE_PATH/src/basemath/trans3.c) and there's
> also a very simple-minded implementation in Octave-forge in the
> special function package.
>
> I trust the Pari implementation more. Perhaps you would like to read
> through it and implement it for the GSL.
>
> Abramowitz and Stegun also have some useful formulae in section 23.2
> (if you have a hard time finding this reference, I can provide it for
> you). I quickly glanced at it, and it looks like Pari uses the Euler
> product to compute zeta(s) for complex s.
>
> HTH,
> - Jordi G. H.