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How to simplify this summation to an incomplete gamma function

by PureStorm
Tags: function, gamma, simplify, summation
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PureStorm
#1
Apr25-14, 10:08 AM
P: 1
Could someone please explain why the following sum simplifies to the following?



=

As far as I can see, this sum does not correlate to the formula for incomplete gamma function as a sum. I'd appreciate any help as the incomplete gamma function is somewhat beyond the scope of my current course.



P.S. I managed to do it eventually. The key was recognising that n-k could be substituted for k as k varies from 0 to n.
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Greg Bernhardt
#2
May4-14, 10:22 PM
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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
JJacquelin
#3
May8-14, 03:47 AM
P: 759
In attachment, we refer to a property of the incomplete gamma function, Eq.(2) in :
http://mathworld.wolfram.com/Incompl...aFunction.html
Attached Thumbnails
Sum.JPG  


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