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 April 29th, 2012, 12:27 PM #1 Member   Joined: Aug 2011 Posts: 71 Thanks: 0 Calculation of sum Help me please to calculate/approximate the following sum: $\sum_{k=0}^l(l-2k)^q \frac{\Gamma(l+1)}{\Gamma(k+1)\Gamma(l-k+1)}$ for any $q\geq 2$ Thank you in advance.
 April 29th, 2012, 12:44 PM #2 Global Moderator   Joined: May 2007 Posts: 6,728 Thanks: 689 Re: Calculation of sum Does n = l? In that case for odd q's the answer is 0.
 April 29th, 2012, 04:12 PM #3 Member   Joined: Aug 2011 Posts: 71 Thanks: 0 Re: Calculation of sum Yes, you are right. $n=l$. But what about even $q$. And $q \in R$?
April 30th, 2012, 01:09 PM   #4
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Re: Calculation of sum

Quote:
 Originally Posted by Anton29 Yes, you are right. $n=l$. But what about even $q$. And $q \in R$?
Sorry - can't help. I don't believe there is any closed form expression.

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