Hello,
How can you prove that:
$\displaystyle \Gamma(x) \cdot \Gamma(1-x) = \dfrac{\pi}{sin(\pi x)}$ ?!
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Hello,
How can you prove that:
$\displaystyle \Gamma(x) \cdot \Gamma(1-x) = \dfrac{\pi}{sin(\pi x)}$ ?!
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.
Thanks. I found an acceptable proof.
$\displaystyle \displaystyle \frac{1}{\Gamma(x)}=xe^{\gamma x}\prod_{n=1}^{\infty} \left(\left(1+\frac{x}{n}\right)e^{-x/n}\right)$
Why is that?
OMG @@
I did not reach this level xD
Thanks anyway :)
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