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December 26th, 2011, 05:05 PM   #1
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approximation for the sum

Find approximation for the folowing sum (not use Stirling's formula):
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December 26th, 2011, 07:11 PM   #2
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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...
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December 27th, 2011, 01:29 PM   #3
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Re: approximation for the sum

I suggest you try using ?(n+1/2)=(n-1/2)(n-3/2)...?(1/2) and similarly for ?(k-1/2).
Also ?(n-k+1)=(n-k)!
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December 27th, 2011, 01:52 PM   #4
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Re: approximation for the sum

I have got:

now using Stirling's approximation:
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December 27th, 2011, 01:53 PM   #5
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Re: approximation for the sum

But I still have no idea how to approximate the last sum...
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December 28th, 2011, 01:11 PM   #6
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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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