Hello,

How can you prove that:

$\displaystyle \Gamma(x) \cdot \Gamma(1-x) = \dfrac{\pi}{sin(\pi x)}$ ?!

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- Jul 15th 2010, 03:02 PMBayernMunichProving one of the Gamma Function's properties ..
**Hello,**

**How can you prove that:**

**$\displaystyle \Gamma(x) \cdot \Gamma(1-x) = \dfrac{\pi}{sin(\pi x)}$ ?!** - Jul 15th 2010, 03:34 PMmr fantastic
This is a well known formula: Reflection formula - Wikipedia, the free encyclopedia

I don't plan to re-invent the wheel. You will find it proved in many textbooks that deal with this sort of stuff (go to your your institute's library) and I have no doubt a Google search will turn up many websites that prove it. - Jul 15th 2010, 05:08 PMchiph588@
- Jul 16th 2010, 02:55 AMBayernMunich
**Thanks. I found an acceptable proof.** - Jul 16th 2010, 03:15 AMAlso sprach Zarathustra
$\displaystyle \displaystyle \frac{1}{\Gamma(x)}=xe^{\gamma x}\prod_{n=1}^{\infty} \left(\left(1+\frac{x}{n}\right)e^{-x/n}\right)$

Why is that? - Aug 24th 2010, 10:07 AMBayernMunich
OMG @@

I did not reach this level xD

Thanks anyway :) - Dec 14th 2010, 04:42 PMchiph588@
Sorry for bringing this thread back from the dead. I just noticed this question went unanswered. I wrote you the answer (and more!) in this pdf file.

Attachment 20110 - Dec 15th 2010, 06:41 AMAlso sprach Zarathustra