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Help me please to prove the following inequality

For $x,y>1, x \neq y$. $$ \frac{1}{\Gamma(x)\Gamma(y)}\leq 2\sqrt{2\pi}\frac{\sqrt{x+y}}{\Gamma(x+y)}. $$

Thank you.

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The inequality does not hold, just try it for $x=3,y=3$. –  Mhenni Benghorbal Nov 7 '12 at 5:11
    
Sorry, I forgot condition that $ x \neq y$. –  user202312 Nov 7 '12 at 15:44
2  
Nevertheless, the inequality does not hold. (Did you even try to check it on some simple values of $x$ and $y$?) –  Did Nov 7 '12 at 16:20
    
en.wikipedia.org/wiki/Beta_function –  JavaMan Nov 7 '12 at 16:39
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