Can the Gamma Function Summation Be Simplified for 0<Re(s)<1?

Thread starter rman144
Start date Jul 15, 2009
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Function Gamma Gamma function Summation

Jul 15, 2009

rman144

I need to find a way to sum/ a closed form representation for:

\sum^{N}_{n=1}\frac{\Gamma(n-s)}{\Gamma(n+s)}

0<Re(s)<1

Thanks for the help in advance.

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Jul 15, 2009

CRGreathouse

Science Advisor

Homework Helper

http://www.wolframalpha.com/input/?i=Sum[Gamma[n-s]/Gamma[n+s],{n,1,N}]

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