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

Dieter Kaiser drdieterkaiser at web.de
Mon Feb 23 16:05:19 CST 2009

```Am Montag, den 23.02.2009, 16:41 -0500 schrieb Raymond Toy:
> 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).