# [Maxima] Extension of the integrator - special functions

Dieter Kaiser drdieterkaiser at web.de
Sat Nov 22 18:55:17 CST 2008

```-----Ursprüngliche Nachricht-----
Von: willisb at unk.edu [mailto:willisb at unk.edu]
Gesendet: Sonntag, 23. November 2008 00:15
An: Dieter Kaiser
Cc: maxima at math.utexas.edu
Betreff: Re: [Maxima] Extension of the integrator - special functions

> I know nothing about pattern matching mechanism in the integration
> code, but I wonder if an alternative to special-casing dozens of
> special functions would be to convert the special functions to
> hypergeometric form, (try to) integrate, (optionally) convert from
> hypergeometric form to special function (Bessel, ...)  form? There are
> dozens of special functions--building pattern matching for all of
> them seems like a great deal of (error-prone) work.

Yes, it might be possible to get a lot of integrals by transforming the
integrands to a hypergeometric representation and integrate that representation.
The code of specint does it. I will have a look at this point too.

But you have to use the pattern matching mechanism to analyse the integrand too.
All of the work of the integrator in the routines of sinint or specint is based
on pattern matching mechanism. When you have found the pattern of the integrand
you can transform it or simply return a solution.

The point is to find the most general pattern for which we know general
solutions.

A next task is to have a look at the code which implement the general rules for
integration like partial integration, substitution of a variable, transformation
rules ... Of course the transformation to a hypergeometric representation has to
be recognized too.

Dieter Kaiser

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