for n =0,1,2,...

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- Mar 12th 2010, 07:44 AMRandom Variablea challenging integral (perhaps)
for n =0,1,2,...

- Mar 12th 2010, 08:12 AMKrizalid
put and your integral equals thus

on the last integral let and get that thus - Mar 12th 2010, 08:36 AMRandom Variable
- Mar 12th 2010, 08:57 AMRandom Variable
and for anyone who cares

and obviously

and - Mar 12th 2010, 09:00 AMKrizalid
note that i never said that your integral equals the latter was because is even, what i actually did was

and that yields the same you got. - Mar 12th 2010, 09:04 AMRandom Variable
- Mar 12th 2010, 10:03 AMPaulRS
A general formula can be found for:

Remember hence:

Note that: let ; then :

Thus: - that is to say multiplied by the coefficient of of that polynomial in there - (*)

(*) Because is for and 0 for all other integer value of .

In particular then:

- , since our answer is the number of pairs of integers (x, y) with such that , fix a valid and that determines .