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 <[EMAIL PROTECTED]>
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.
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