On Mon, Mar 25, 2013 at 5:37 PM, Richard Fateman
<fateman at eecs.berkeley.edu>wrote:
> On 3/22/2013 8:24 AM, Jean-Claude Arbaut wrote:
>
> ...Is it possible to simplify gamma(x)*gamma(1-x) ?...
>
> I guess you want to know if there is some program that will
> magically convert that expression to %pi*csc(%pi*x);
> So far as I know, not in Maxima right now.
>
> More generally, most simplifications built in to Maxima have
> to do with a function (e.g. sin, cos, gamma) and its argument.
> ...
> What you are asking about is really more like a simplifier for
> *multiplication* that knows about (products of) gamma functions.
> This would be a more ambitious kind of program....
>
Well, there are already some routines in Maxima to simplify special
products, e.g.
trigreduce(2*sin(x)*cos(x)) => sin(2*x)
minfactorial(x*x!^2/(x+2)!) => x*x!/((x+1)*(x+2))
factcomb(x^3*(x+3)!) => (x+6)!-15*(x+5)!+61*(x+4)!-64*(x+3)!
They could probably be used as models.
Probably not a good idea to incorporate such things into the general
simplifier, though, given its design.
-s