Am Montag, den 08.06.2009, 13:17 -0400 schrieb Dan Gildea:
> > From: Dieter Kaiser <drdieterkaiser at web.de>
> > Subject: New definite integrals and new problems
> >
> > (%i58) integrate(exp(-x)*log(x),x,0,inf);
> > (%o58) -'limit(-%e^-x*log(x)-gamma_incomplete(0,x),x,0,plus)
> >
> > The last step is to get the limit of the above expression which is known
> > to be -%gamma.
>
> To get this limit, we probably need asymptotic expansions of the
> special functions: see e.g. p 80 of Gruntz's thesis.
I have got a paper from Richard Fateman - again many thanks - which
gives three more general algorithm for integrals like the above. The
algorithm are based on the differentiation of the integral
representation of the Gamma, Beta and Incomplete Gamma functions.
I think we have all functionality which is needed to implement these
algorithm.
Dieter Kaiser