What is this function that is related to the Beta function?

Question

where the $\frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}$ is beta function $B(m,n)$ then what is this function $\frac {\Gamma (m)\Gamma (n)}{\Gamma (m-n)}$?

Answer 1

If $m>n$, then

$$ \frac {\Gamma (m)\Gamma (n)}{\Gamma (m-n)}= \frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}\frac{\Gamma(m+n)}{\Gamma(m-n)}= {\prod}_{i=0}^{n}(m-i)\beta(m,n). $$