[Maxima] levin versus ratsum
Michel Van den Bergh
michel.vandenbergh at uhasselt.be
Fri Dec 29 11:22:34 CST 2006
> miguel lopez <miguel39123 <at> hotmail.com> writes:
> Summation of rational functions.
> The theory is, for example, in the handbood of Mathematical Functions.
> The ARPAC proyect has numerical software for computing the polygamma functions.
The main aim of maxima should be to compute them symbolically whenever
> Best Regards,
Thanks for the ref! Unfornutely the only special values of the poly
gammy and psi function that are given are integers and half integers it
seems. So this corresponds to my elementary observation that if in
p(n)/q(n) the roots of q are integers or half integers then the
summation can be done symbolically.
So sum_n 1/(3n+1)^2 (*) can not be done. I computed this sum and it
is related to special values of the di-logarithm (which is a
non-elementary quantity I presume).
On the other hand it is easy to see that sum_n (1/(3n+1)^2+1/(3n+2)^2)
can be expressed in terms of zeta(2). May this follows by applying
the "reflection formula" or "multiplication formula"? These give linear
relations between the polygamma functions.
I am not sure yet that just expressing everything in poly gamma
functions is the definite answer. The paper I was referring to seems to
use different methods.
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