simplification of products of gamma functions & bfloat bug
Subject: simplification of products of gamma functions & bfloat bug
From: Dieter Kaiser
Date: Mon, 23 Feb 2009 22:11:35 +0100
Am Sonntag, den 22.02.2009, 18:50 -0600 schrieb Barton Willis:
> Is there a Maxima function that simplifies (%o47) to 1? The composition
> minfactorial(makefact(...)) doesn't simplify (%o47) to 1. Also, maybe it
> has already been fixed, but (%o48) shows a bug:
>
> (%o47) (gamma(1/7)*gamma(4/21)*gamma(17/21)*gamma(6/7)-gamma(4/21)*gamma
> (10/21)*gamma(11/21)*gamma(17/21))/(gamma(1/7)*gamma(10/21)*gamma
> (11/21)*gamma(6/7))
The Maxima functions I know can not simplify products of gamma
functions. Perhaps we can implement some rules for the product of gamma
functions. These are some examples
(1) gamma(z)*gamma(w) = factorial(z+w-2)/binomial(w+z-2,z-1)
(2) gamma(z)*gamma(w) = gamma(z+w)*beta(z,w)
(3) gamma(z)/gamma(w) = factorial(z-w)/binomial(z-1,z-w)
(4) gamma(z)/gamma(w) = pochhammer(w,z-w)
But the first rule will not work in the example above, because we get an
undefined factorial(-1). The second rule will simplify to an expression
with the sin function.
Dieter Kaiser