
Help with identity
Posted:
Apr 25, 2013 8:17 AM


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

