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

[Jordi Gutiérrez Hermoso]

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.