Abstract <p> The first boundary value problem is studied for a two-dimensional wave equation ina cylindrical domain. A uniqueness criterion is established. The solution is constructed as the sumof an orthogonal series. When justifying the convergence of the series, the problem of smalldenominators from two positive integer arguments is solved. An estimate for separation from zerowith the corresponding asymptotics is established, which permits proving the convergence of theseries in the class of regular solutions and the stability of the solution.</p>