Extension of the integrator - more integrals with power functions

On 11/21/08, Dieter Kaiser <drdieterkaiser at web.de> wrote:

> I have finished a first step to extend the integrator of Maxima to support more
>  integrals with power functions. First I created a test file with 734 integrals.
>  Maxima is able to solve 241 integrals. I have implemented 10 pattern to support
>  382 additional integrals. There are 111 integrals remaining for which I have not
>  implemented a routine up to now. Because Maxima knows some general integration
>  rules there much more integrals which Maxima now can solve with these
>  extensions.

Tremedous, fantastic, wonderful. Thanks a lot for working on these problems.

>  rtestint.mac, Problem 90:
>
>  Maxima now get a solution for the integral log(x)^k in terms of the Incomplete
>  Gamma function. The expected result of the problem is gamma(k+1). We now get:
>
>  (%i3) assume(k>0)$
>  (%i6) integrate((-log(x))^k,x,0,1);
>  (%o6) 'limit(gamma_incomplete(k+1,-log(x+1)),x,0,minus)
>        -'limit(gamma_incomplete(k+1,-log(x)),x,0,plus)
>
>  This result is equivalent to the expected result gamma(k+1), but Maxima can not
>  calculate the limits for the function gamma_incomplete. It is possible to check
>  the result by inserting the limits for the Log funtion. Perhaps we can improve
>  the routine $limit to get the expected result.
>
>  Can we ignore this problem?

Yes, please adjust rtestint.mac accordingly.

>  So what do you think? Should we extend the integrator?

Yes, please commit these changes.

>  The code is written in a way to support in principle a complex symbol as
>  integration variable (not a complex number like x+%i*y), but Maxima ignores in
>  al lot of cases the declaration as a complex value and does a lot
>  simplifications which are not allowed for complex symbols. Therefore not all of
>  the results are correct for a complex symbol as integration variable. This is
>  not a problem of the integrator but of the simplifier.

Yes, Maxima's inconsistent treatment of complex variables is a serious problem.

Thanks for your help, I appreciate it a lot.

best

Robert Dodier