limit(x^p*exp^(-x),x = infinity)=0
G(p) := Int(x^p*exp^(-x),x = 0 .. infinity)
I used integration by parts by can't get G(p+1)=G(p)
Thank you very much
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Are you sure you have it written correctly.
Replace p with p+1 to get:
We can integrate by parts, let
This is why I questioned G(p+1)=G(p). It is G(p+1)=pG(p). Maybe that's why you couldn't arrive at the correct answer.
Does this help?.
Thank you very much. I've got the same. Must be I wrote it wrong
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).