The constructed approximate solutions of the evolutional equation of the hyperbolic type with degeneracy, the estimate of the error of the approximation is given. 

[1] Babin A.V. Construction and study of solutions of differential equations by methods of the theory of approximation of functions / / Matem. sb. - 1984. - V. 123, № 2. - P. 147-174.

[2] Gorodetsky V.V. Initial value sets of smooth solutions of differential operator equations of parabolic type. - Chernivtsi: Ruta, 1998. - 219 p.

[3] Gelfand I.M., Shilov G.E. Spaces of basic and generalized functions. - M.: Fizmatgiz, 1958. - 307 p.

[4] Gorbachuk V.I., Gorbachuk M.L. Boundary value problems for differential-operator equations. - Kyiv: Nauk. Dumka, 1984. - 284 p.

[5] Goma N.M., Gorodetsky V.V. Evolutionary equations with a harmonic oscillator in spaces of type $S$ and $S'$ // Scientific Bulletin of Chernivtsi University: 3b. scientific works. Issue. 269. Mathematics. - Chernivtsi: Ruta, 2005. - P. 13 - 25.

[6] Vainerman L.I. Hyperbolic equations with degeneration in Hilbert space // Siberian Math. J. - 1977. - Vol. 18, № 4. - P. 736-746.

[7] Suetin P.K. Classical orthogonal polynomials. - S.: Nauka, 1976. - 328 p.

[8] Shoge G. Orthogonal polynomials. - M.: Fizmatgiz, 1962. - 500 p.