
Re: Help with identity
Posted:
May 2, 2013 4:06 PM


On Thursday, April 25, 2013 5:17:47 AM UTC7, 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)] > > > > 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
Maybe nobody ever did the integrals to get the series; maybe in the distance past somebody obtained the series, perhaps as part of a larger project, and then asked themselves: hmmmm ... I wonder if the series can be expressed in closed form? Then maybe they discovered the function you have started with.

