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

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Mike Trainor

Posts: 28
Registered: 4/21/13
Help with identity
Posted: Apr 25, 2013 8:17 AM
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Would greatly appreciate any pointers to proving the following
identity that I came across in Bateman's book on partial
differential equations:

sinh(x)/(cosh(x) - cos(y) = 1 +

sum{n, 1, inf} [exp(-nx)*cos(ny)]

It is clearly a simple Fourier expansion in y, but how does
one get the coefficients -- in other words do the integral.

OTOH, it is trival to prove that the RHS can be summed
to give the LHS.

The one out I see it expressing either the trignometric
or hyperbolic functions as the other type by using an
imaginary arguments, but I could not get anywhere.

Also 0<= x < inf and 0 <= y <= 2 pi


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