In the 1970's, the hypergeometric approach was worked on by Yannis Avgoustis
-- http://dspace.mit.edu/handle/1721.1/16269 . If I remember correctly, the
most difficult problem (which I don't think was solved very completely) was
precisely simplifying the hypergeometric representation back to more
elementary functions in the (many) cases where that was possible. Perhaps we
can do a better job now.
-s
On Tue, Mar 9, 2010 at 16:08, Dieter Kaiser <drdieterkaiser at web.de> wrote:
> Am Dienstag, den 09.03.2010, 12:59 -0500 schrieb Raymond Toy:
> > On 2/28/10 1:53 PM, Dieter Kaiser wrote:
> > > I have implemented a small extension to get more integrals for special
> > > functions. The idea is to support a special routine which is looked up
> > > in the routine INTFORM, if Maxima does not get a result for the desired
> > > special function.
> > >
> > > This is the implementation in INTFORM:
> > >
> > >
> > [snip]
> > > The testsuite has no problems. We get no slow down, because the new
> code
> > > is only executed, if a special function is part of the integrand. We
> > > only get new integrals.
> > >
> > > If the implementation is of interest I would like to commit the code.
> > >
> > Is there any kind of general theory we can use for these integrals?
> > Kind of like how specint works by converting the integrand to a
> > hypergeometric form and integrating that? I mostly just curious.
>
> One more general approach is to integrate the hypergeometric
> representation of special functions. The only problem is that we need to
> extend the hypergeometric code to get a lot more simplifications in
> terms of special functions too.
>
> > Another thing that we might want to look into is TILU (table of
> > integrals by lookup). Richard Fateman has obtained permission for us to
> > use that and he sent out the code sometime ago. I meant to look into
> > integrating that into maxima, but I never got around to it. (Some
> > design issues need investigating, like where the integrals are stored.
> > As part of maxima? Some webserver somewhere? Something else?)
>
> Yes, I have thought about this too. Therefore, I have hesitated to
> commit anything. I had a look at the code already introduced with
> abs_integrate and I think it might be much better to extend this code
> and not the Lisp integrator.
>
> Another point is, that the integrator might be improved further in its
> core functionality to support more general problems.
>
> Dieter Kaiser
>
>
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