On Sunday 18 January 2009 19:57:32 Robert Dodier wrote:
> On 1/17/09, Alexey Beshenov <al at beshenov.ru> wrote:
> > Maybe we can extend compar.lisp by the following stuff:
>
> I';m not familiar with the code in question, so I don't know what's
> new here. If you post a diff, it will be obvious what's changed.
sign-zeta is my function; I'm not sure how to add it to the
sign-related functions from compar.lisp in an appropriate way.
Also there is another interesting issue related to the mentioned
integral:
(%i1) integrate (t^3/(exp(t)-1), t, 0, inf);
Is zeta(3) positive, negative, or zero?
p;
(%o1) 'limit(6*li[4](%e^t)-6*t*li[3](%e^t)+3*t^2*li[2](%e^t)
+t^3*log(1-%e^t)-t^4/4,t,inf)
-%pi^4/15
The corresponding indefinite integral indeed should contain
polylogarithms, but it would be nice to see the definite integral
evaluated since it is convergent and the right answer is %pi^4/15.
(I'm wondering if other integrators take this limit or they rely on
another techniques.)
--
Pungenday, Chaos 18 YOLD 3175
Alexey Beshenov http://beshenov.ru/