Can someone explain how much of this is new? It would be nice for people to
say "maxima can't do this but I can."
Commercial macsyma finds ((psi[1]((1/3)))/9) - 1 as the result of
Closedform (sum(1/(3*n+1)^2,n,1,inf) ).
I thought that sums of rational functions were entirely resolved some time
ago, much as integration of rational functions was resolved. Instead of
doing partial fraction decomposition, one does a "shift-free" decomposition,
and then the results are easily summed either to rational or polygamma terms
See
www.cs.berkeley.edu/~fateman/282/lects/19.ppt
Maybe this is novel because it works for summation to infinity?
Or is it just another way to do some set of problems that can already be
done?
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of miguel lopez
> Sent: Friday, December 29, 2006 12:10 PM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] levin versus ratsum
>
> Michel Van den Bergh <michel.vandenbergh <at> uhasselt.be> writes:
>
>
> > http://math.depaul.edu/~mash/telescopetams.pdf
> >
> > Regards,
> > Michel
> >
> Thanks for the reference. It gives neccesary and sufficient conditions
> for a
> rational function over the integer to be telescopic. The paper is very
> easy to
> read, i think that even high school pupils can get the general ideas.
>
> Perhaps i can improve ratsum to test cases in which the symbolic
> summation
> gives a rational number, like in the paper.
>
> Best regards.
>
> Just for fun, you consider sum_n 1/(3n+1)^2 (*) and then sum_n
> (1/(3n+1)^2+1/(3n+2)^2), the first one is sum_ an and the last one is
> sum b_n with b_n = a_n + a_(n+1) so trivially sum bn = (2* sum a_n) - a_1.
>
>
>
> -M
>
>
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