# [Maxima] simplification of products of gamma functions & bfloat bug

Raymond Toy raymond.toy at stericsson.com
Mon Feb 23 15:41:14 CST 2009

Dieter Kaiser wrote:
> 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.
>
>
I did the transformation to beta functions by hand yesterday.  I
couldn't get the trig functions to simplify to 1 either.   The trig
functions involved terms like sin(n*%pi/21) and cos(n*%pi/21).

Ray