How to simplify this summation to an incomplete gamma function

[PureStorm]

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.

 

[Greg Bernhardt]

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]

In attachment, we refer to a property of the incomplete gamma function, Eq.(2) in :
http://mathworld.wolfram.com/IncompleteGammaFunction.html