where the $\frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}$ is beta function $B(m,n)$ then what is this function $\frac {\Gamma (m)\Gamma (n)}{\Gamma (m-n)}$?
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1Rather like asking "if $\frac{(m+n)!}{m!n!}$ is a binomial coefficient then what is $\frac{(m-n)!}{m!n!}$ – Henry Feb 07 '13 at 09:06
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If $m>n$, then
$$ \frac {\Gamma (m)\Gamma (n)}{\Gamma (m-n)}= \frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}\frac{\Gamma(m+n)}{\Gamma(m-n)}= {\prod}_{i=0}^{n}(m-i)\beta(m,n). $$
Mhenni Benghorbal
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