Classical and generalized solutions of a mixed problem for a nonhomogeneous wave equation

A.N. Krylov's ideas concerning convergence acceleration for Fourier series are used to obtain explicit expressions for the classical solution of a mixed problem for a nonhomogeneous equation and explicit expressions for a generalized solution in the case of arbitrary summable $q(x)$, $\varphi (x)$, $\psi (x)$, and $f(x,t)$ .