
Re: Help with identity
Posted:
Apr 26, 2013 9:31 AM


On 26/04/2013 13:10, Mike Trainor wrote:
> Find the Fourier series expansion in y of > > sinh(x)/(cosh(x)  cos(y)). > > As I said in my first note, Bateman *gives* the answer > by stating it without proof. I am looking for the proof.
As David said, summing the claimed answer to give this function *is* a proof.
> It comes down to doing the integral of > > cos(ny)/(cosh(x)  cos(y)) > > from 0 to 2 pi, for integer n, where x => 0.
How about integrating z^{n1}/(cosh(x)  (z+1/z)/2) over the unit circle in C?

