On 3/22/2013 8:24 AM, Jean-Claude Arbaut wrote:
> Hello all,
>
> Is it possible to simplify gamma(x)*gamma(1-x) ?
> More generally, are there functions to simplify expressions involving
> "special functions", not only rat/trig ?
>
> Jean-Claude
>
>
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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.
Thus sin(n*%pi)... or particular values for bessel functions
or hypergeometric functions. If they are not already there,
they can sometimes be added by tellsimp or tellsimpafter.
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.
To look at an expression globally and apply transformations like
ratsimp or factor or trigsimp is generally a far
more difficult matter. Some heuristic methods can be applied to
do transformations in some kind of "hill climbing" fashion to
find the smallest expression or the one with certain goals
using (say) only exponentials and log, and not arctrig functions or
trig functions. etc.
I think there isn't a program like this in Maxima, but one could
be written given the collection of tools available. Hints on how
this might be done can probably be found by looking at documentation for
Maple's simplify() command or Mathematica's FullSimplify[] command.