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## Main Question or Discussion Point

**Orthogonality Property of Hyperbolic functions ???**

Hi all,

I have seen Orthogonal property for trigonomeric functions but I am unsure if there is something similar for sinh() , cosh() ? . I know that the integral of inner product of the two functions should be zero for them to be called as orthogonal.

I am asking this question because if one applies Variable separable form of F(x)G(y) to solve a laplace equation, then one always gets one of F(x) or G(y) to be hyperbolic. With this being the case ,doesn any body know how to extract coefficients from series form of solution

of laplace equation when (say) only sinh(kx) is remaining :

for e.g Summation {Pn cosh(kx) } =phi . How to extract Pn ?

Had it been Summation {Pn cos(kx) } =phi ,then one can use orthogonal property of trigonometric function .

I hope ,I am clear.

Thanks ,

A.S