> From: Richard Fateman>
> I just had occasion to try hgfred. There are errors in
> simplification in this program that allow it to generate
> subexpressions like (1- -x) or even (1 - -36). Someone is producing
> expressions with incorrect ((mtimes simp)..) headers.
> Unfortunately I didn't catch the examples before my system
> crashed. But there are other probs.
>
> as an example, consider
> i3(m,k,a,x):=(x^(1 + m)*(a^2 + x^2)^k*hgfred([(1 + m)/2, -k],
> [1 + (1 + m)/2], -(x^2/a^2))/((1 + m)*(1 + x^2/a^2)^k));
>
> i3(m,k,a,x)
> should, I think, be the integral of x^m*(x^2+a^2)^k.
>
> The following example (and many others) give odd messages
> like SIMP2F1-WILL-CONTINUE-IN
>
> i3(2,3/2,a,x)
>
> i3(0,1,a,x) [also says FAIL-1-IN-C-1-CASE]
> i3(1,1/2,a,x) [gives "non-variable 2nd argument to diff, -x^2/a^2]
>
> also some of the answers come out in terms of jacobi_p
> functions, but diff does not know about them.
Coincidentally I was looking through the code in hypgeo.lisp as I
want to document the special functions defined and used by hgfred
and specint there. I also downloaded a copy of Yannis Avgoustis'
thesis from http://dspace.mit.edu/handle/1721.1/16269
At present there are multiple versions of some of the special
functions. For example:
%he[n](x) and hermite(n,x) for Hermite polynomials
%t[n](x) and chebechev_t(n,x) for Chebychev polynomials
%p[n,a,b](x) and jacobi_p(n,a,b,x) for Jacobi polynomials
maxima cannot differentiate the older % forms, and I have not (yet)
found any use of them outside hgfred and specint.
Once I understand the code better I may propose a consolidation.
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