limit(x^p*exp^(-x),x = infinity)=0

G(p) := Int(x^p*exp^(-x),x = 0 .. infinity)

show that

G(p+1)=G(p)

I used integration by parts by can't get G(p+1)=G(p)

Thank you very much

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- Aug 26th 2006, 02:57 PM #1

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- Aug 26th 2006, 03:44 PM #2

- Aug 26th 2006, 04:08 PM #3

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- Aug 26th 2006, 04:55 PM #4

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If you want to get into formal detail about convergence check here

(I did make a mistake in the proof, that the second part when I evaluate by parts cannot be done. However, you can increase the domain in part one to correct the proof).

- Aug 26th 2006, 06:21 PM #5