Subject: Numerical evaluation of zeta and psi functions
From: Andrej Vodopivec
Date: Sat, 30 Dec 2006 19:32:55 +0100
On 12/30/06, Andrej Vodopivec <andrej.vodopivec at gmail.com> wrote:
> I also think that maxima is using incorrect reflection formula for
> negative values of z:
>
> psi[n](z) = (-1)^n*psi[n](-z) + (-1)^n*diff(cot(-%pi*z), z, n)
>
> I think this should be
>
> psi[n](z) = (-1)^n*psi[n](1-z)+(-1)^n*diff(cot(%pi*(1-z)), z, n)
Sorry, this should be
psi[n](z) = (-1)^n*psi[n](1-z)+(-1)^n*%pi*diff(cot(%pi*(1-z)), z, n)
the factor %pi is missing in symbolic simplification code. Numeric
code has %pi but has z instead of 1-z on the right side.
Andrej