Daniel Ward
Posted on Thursday, 08 May, 2003 - 08:03 pm:
Given that
I(n) = ó
õ 		1

0 
 (x2 + a2)-n
show that
(2na2) I(n+1) = (2n - 1)I(n) + (1 + a2)-n.
Splitting up to do it by parts leaves you with a nasty arctan wandering around loose.

Help!

Oscar Randal-Williams
Posted on Friday, 09 May, 2003 - 10:35 am:
If you write LaTeX Image then LaTeX Image.

If you then use parts on the first integral it works fine.
David Loeffler
Posted on Friday, 09 May, 2003 - 03:58 pm:
When doing the integral by parts, it might help to split it up as
(x) ( x / (x2 + a2 )n+1 ), as it is obvious how to integrate the second factor. Using (x2 ) ( 1 / (x2 + a2 )n+1 ) will give you the nasty arctans.