Further improvements to integral property code

Hello David,

nice to see that the generalizations of the code for integrals on the property
list works so nice.

Concerning the Hypergeometric functions I would suggest to introduce a
simplifying functions which can use hgfred to simplify and have the following
notation:

hypergeometric([a1,a2,...],[b1,b2,....],z)

This general function could be specialized for the most important cases like:

hypergeometric_2f1(a1,a2,b,z)

We can support the hypergeomtric representation on the property list too. This
representation could be looked up by the integrator and then integrated. One big
problem is that hgfred produces a lot of asksign. I think the code of hgfred can
be improved.

The technique to lookup the hypergeometric representation would be very
interesting for the Laplace transformations in $specint too. The code of
$specint can be much simplified using a lookup algorithm. By the way I think it
would be nice a feature for the Maxima User to get the hypergeometric
representation of a function.

Dieter Kaiser

-----Urspr?ngliche Nachricht-----
Von: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] Im
Auftrag von Billinghurst, David (RTATECH)
Gesendet: Sonntag, 4. Januar 2009 04:46
An: maxima at math.utexas.edu
Betreff: Re: [Maxima] Further improvements to integral property code

> From: David Billinghurst
> 
> I have spent some time tidying up the integral property code 
> that Dieter and I have been working on recently.  It now 
> works for functions with an arbitrary number of arguements.
> 
> I then extended it to work for:
>  - cases where the integral property is a function, and
>  - subscripted functions.
>
> As a further test I had a go at the 0F1 hypergeometric 
> function with the following code (which is not in CVS).

... and here is naive code for a pFq hypergeometric function.
I don't know enough about these functions to know if we should
do if any of the terms in the denominator are zero.


(defprop $%f
  ((p q p-list q-list z)
   nil
   nil
   nil
   nil
   (lambda (p q p-list q-list unused)
     (cond 
      ((and ($integerp p) 
	    ($integerp q)
	    (= ($length p-list) p)
	    (= ($length q-list) q))
       (let* ((p-list-1 
	       `((mlist) ,@(map 'list (lambda (x) (sub x 1)) (cdr
p-list))))
	      (q-list-1 
	       `((mlist) ,@(map 'list (lambda (x) (sub x 1)) (cdr
q-list)))))
	      `((mtimes)
		,(div
		  `((mtimes) ,@(cdr q-list-1))
		  `((mtimes) ,@(cdr p-list-1)))
		((mqapply) (($%f array) ,p ,q) 
		 ,p-list-1
		 ,q-list-1
		 z))))
      (t nil))))
  integral)

With this:

(%i31) integrate(%f[2,2]([a1,a2],[b1,b2],x),x);
        %f    ([a1 - 1, a2 - 1], [b1 - 1, b2 - 1], x) (b1 - 1) (b2 - 1)
          2, 2
(%o31)  ---------------------------------------------------------------
                               (a1 - 1) (a2 - 1)

(%i33) integrate(x*%f[2,2]([a1,a2],[b1,b2],x^2),x);
                                                   2
       %f    ([a1 - 1, a2 - 1], [b1 - 1, b2 - 1], x ) (b1 - 1) (b2 - 1)
         2, 2
(%o33) ----------------------------------------------------------------
                             2 (a1 - 1) (a2 - 1)

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