[Maxima] Extension of the integrator - integration of special functions
drdieterkaiser at web.de
Fri Dec 5 18:21:40 CST 2008
I have committed some code to do a first step to extend the integrator to give
results for some special functions.
At first the integrals for the Incomplete Gamma function, the Exponential
Integrals and the Error functions are implemented.
I have put the integral of the erf function on the property list too. The code
of rischint also support the erf function (but not erfc and erfi). Therefore for
some integrals of the erf function the algorithm has changed, but we have no
errors with the testsuite.
In principle the algorithm work for every special function. Furthermore we can
support a Maxima User function which allow the extension of the integrator for
User defined functions too.
One restriction is, that only functions with one argument are generally
supported at this time. Only for the functions gamma_incomplete and
expintegral_e code is implemented to support a function with two arguments. This
can be generalized.
Next I have done some first tests to extend the integrator to give results for
the hypergeometric functions. If we do this extension general enough we can use
a transformation to a hypergeometric function to get more results. Also the code
of specint can be improved, when we have more general and simplifying
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