Fantastic! Maxima is improving very fast!
Michel
Andrej Vodopivec wrote:
> On 12/31/06, Michel Van den Bergh <michel.vandenbergh at uhasselt.be> wrote:
>> >
>> > >/
>> > />/ About computing the sum of rational functions by
>> polygamma functions:
>> > />/ first this needs to compute the roots of the denominator --> a
>> numerical method,
>> > />/ so the obtained precision is not that os polygamma but that of
>> the numerical
>> > />/ method for computing the roots of the denominator.
>> > />/
>> > />/
>> > />/
>> > /Maxima can work with algebraic integers! tellrat is the command.
>> >
>> >
>>
>> And a common subcase would be where the roots are half integers. In that
>> case Maxima can use
>> simplication to obtain the symbolic result in terms of the zeta
>> function.
>
> I will soon commit a new version of closed_form (along with some
> bugfixes for polygamma in maxima) to cvs. It will convert sums of
> rational functions to psi functions. Maxima knows enough about psi to
> simplify to zeta and other functions when it is possible. Here's what
> I have currently:
>
> (%i2) sum(1/n/(2*n+1), n, 1, inf)$
> (%i3) closed_form(%);
> (%o3) 2-2*log(2)
> (%i4) sum(n/(3*n+1)/(2*n+1)^2, n, 1, inf)$
> (%i5) closed_form(%), ratsimp;
> (%o5)
> -(12*sqrt(3)*log(3)-16*sqrt(3)*log(2)-sqrt(3)*%pi^2+4*%pi)/(8*sqrt(3))
>
> Andrej