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Topic: Help with identity
Replies: 15   Last Post: May 9, 2013 7:13 AM

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Robin Chapman

Posts: 301
Registered: 5/29/08
Re: Help with identity
Posted: Apr 26, 2013 9:31 AM
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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^{n-1}/(cosh(x) - (z+1/z)/2)
over the unit circle in C?






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