# Eigenfunction expansion solution to a PDE with a constant non homogeneous term

I'm wondering if the method of finding a solution to a nonhomogeneous PDE by the method of eigenfunction expansion works if the nonhomogeneous term is a constant, rather than a function of the independent variables? For example, in a hyperbolic PDE with x and t as the independent variables the eigenfunctions might be something like $\sum_{n=1}^\infty sin(n\pi x)$, and to create an eigenfunction expansion of the nonhomogeneous term I have to solve for the coefficients A of $\sum_{n=1}^\infty A sin(n\pi x) = B$ by using the orthogonality of sines, where B is the constant nonhomogeneous term. I guess I'm having trouble seeing how an infinite series of sines could converge to a constant - I know in a Fourier series one has to solve for the "DC component" separately.

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