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

