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?