Date: Aug 22, 2012 7:42 AM
Author: Brad Cooper
Subject: Derivation of limit of infinite quotient

If

f(n) = product(x^2-k^2*PI^2, k=1..n) and
g(n) = product(x^2+k^2*PI^2, k=1..n)

then limit n -> infinity of f(n)/g(n) = sin(x)/sinh(x)

I am looking for a derivation and/or a proof of this.

Could someone please give a pointer to where I can get started on this?

Regards :-)