December 26th, 2011, 05:05 PM  #1 
Member Joined: Aug 2011 Posts: 71 Thanks: 0  approximation for the sum
Find approximation for the folowing sum (not use Stirling's formula): 
December 26th, 2011, 07:11 PM  #2 
Member Joined: Aug 2011 Posts: 71 Thanks: 0  Re: approximation for the sum
Ok. I've tried with Stirling's formula as well. But then I have a problem to calculate the sum...

December 27th, 2011, 01:29 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716  Re: approximation for the sum
I suggest you try using ?(n+1/2)=(n1/2)(n3/2)...?(1/2) and similarly for ?(k1/2). Also ?(nk+1)=(nk)! 
December 27th, 2011, 01:52 PM  #4 
Member Joined: Aug 2011 Posts: 71 Thanks: 0  Re: approximation for the sum
I have got: now using Stirling's approximation: 
December 27th, 2011, 01:53 PM  #5 
Member Joined: Aug 2011 Posts: 71 Thanks: 0  Re: approximation for the sum
But I still have no idea how to approximate the last sum...

December 28th, 2011, 01:11 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716  Re: approximation for the sum
I can't help you with your approach. I suggest you try using the information I gave you. With a little manipulation you will have no half integer gammas. You will have a lot of factorals and powers of 2. It may not work, but it will be clearer.


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