It should be in the sub-forum "Interesting Math Problem" but there is no such place for me to post (Rofl) It is not very hard but the answer is extremely elegant !!

Show that

and

Printable View

- August 26th 2009, 04:49 AMsimplependulumInteresting integral
It should be in the sub-forum "Interesting Math Problem" but there is no such place for me to post (Rofl) It is not very hard but the answer is extremely elegant !!

Show that

and - August 26th 2009, 03:13 PMNonCommAlg
- August 26th 2009, 05:24 PMluobo
- August 26th 2009, 07:32 PMNonCommAlg
let be an integer. let we have: call this

now let then and therefore integration by parts gives us:

put this in to get:

that's what i got and i think it's good enough! of course this recurrence relation will also give us a general formula for but i'm not going to do it! (Shake) - August 26th 2009, 08:10 PMsimplependulum
Thanks for your corrections (Happy) , i think i need to have a double check after i finish a problem next time . (Crying)

- August 27th 2009, 05:31 AMluobo
- August 27th 2009, 06:53 AMsimplependulum
- August 27th 2009, 01:29 PMluobo