Board index Computation of Series Compute $\Gamma(x)\Gamma(y)\Gamma(z)$

## Compute $\Gamma(x)\Gamma(y)\Gamma(z)$

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### Compute $\Gamma(x)\Gamma(y)\Gamma(z)$

Thu Feb 16, 2017 4:59 am

Posts: 1
Hi everyone!!, This is my first post here.. So, I don't know this is the right section. Anyway, How I compute this product, where $a,b,c$ such that $1\leq a\leq d-1$, $1\leq b\leq d-1$ and $1\leq c\leq d-1$. I try to use reflection formula, and the basic identities of gamma function

$$\dfrac{\Gamma\left(\dfrac{a}{d}\right)\Gamma\left(\dfrac{b}{d}\right)\Gamma\left(\dfrac{c}{d}\right)}{\Gamma\left(\dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}\right)}$$

I need write this as sin function with some constan. Any hint will be appreciated. Thanks!
Last edited by celeste_ on Thu Feb 16, 2017 11:08 pm, edited 2 times in total.