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

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David C. Ullrich

Posts: 3,138
Registered: 12/13/04
Re: Help with identity
Posted: Apr 25, 2013 10:56 AM
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On Thu, 25 Apr 2013 08:17:47 -0400, Mike Trainor
<mtrainor@hotmail.com> wrote:

>
>
>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)


Unclear what you mean, since the parentheses are not
balanced. Maybe 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.


??? If you can do that then you've proved the identity;
what's the problem?

>
>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
>
>tia
>mt





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