we have thus finally as required.
Like before, I've come up with this integral (with several difficulties though...) by a probabilistic way. I'll show it later. But I ask you to find it ^^
Yes, I can see Tessy coming with complex analysis and actually, I can do it too ^^'
then substitute to get: but we have and thus:
which gives us: now change the order of summation to get:
but it's easy to see that and the result follows. i'm pretty sure there are easier ways to prove this result. maybe some of you want to try it?