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

 Messages: [ Previous | Next ]
 AP Posts: 137 Registered: 3/4/09
Re: Help with identity
Posted: May 8, 2013 2:29 AM

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

not
1+2sum{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
>
>tia
>mt

Date Subject Author
4/25/13 Mike Trainor
4/25/13 David C. Ullrich
4/26/13 Mike Trainor
4/26/13 Robin Chapman
5/1/13 Mike Trainor
5/1/13 Mike Trainor
5/2/13 Robin Chapman
5/2/13 Robin Chapman
5/2/13 Mike Trainor
5/2/13 Mike Trainor
4/26/13 David C. Ullrich
4/29/13 Mike Trainor
5/2/13 RGVickson@shaw.ca
5/8/13 AP
5/8/13 Virgil
5/9/13 Mike Trainor