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A superposition of these solutions is a series u(x,y) = c 0y+ X ∞ n=1 c n sinh nπy L cos nπx L, where c 0,c 1,c 2,...are constants. Substituting the series into the boundary condition u(x,H) = f(x), we get f(x) = c 0H+ X ∞ n=1 c n sinh nπH L cos nπx L. The right-hand side is a Fourier cosine series on the interval [0,L]. Therefore the ...
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