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

Printable View

- Aug 26th 2006, 03:57 PMsimfonijaPlease help
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 - Aug 26th 2006, 04:44 PMgalactus
Are you sure you have it written correctly.

Replace p with p+1 to get:

We can integrate by parts, let

=

Therefore,

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?. - Aug 26th 2006, 05:08 PMsimfonija
Thank you very much. I've got the same. Must be I wrote it wrong

Great help! - Aug 26th 2006, 05:55 PMThePerfectHacker
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, 07:21 PMsimfonijaThank you so much
:)