The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 137
Registered: 3/4/09
Re: Help with identity
Posted: May 8, 2013 2:29 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Thu, 25 Apr 2013 08:17:47 -0400, Mike Trainor
<> 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)]

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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.