plate bending, Fadle-Papkovich functions, analytical solutions.

Examples of expansions Lagrange function of Fadl-Papkovich arising in the solution of a boundary value problem of the bending of the semistrip, of which two opposite ends of the free and the boundary conditions at the end may be different. Based on the results of [1-3] for the planar problem of elasticity theory, you can get closed analytic solutions of various boundary value problems of the theory of bending of thin plates, exact solutions which were not found. These solutions are presented in the form of series of functions of Fadl-Papkovich. Decision coefficients of expansions are using systems of functions, biorthogonol to the functions of the Fadl-Papkovich. Functions Fadl-Papkovich are a generalization of trigonometric Fourier series and the expansion in him (decomposition of Lagrange) are a generalization of expansions in trigonometric Fourier series.

Abrukov, Denis Alexandrovich Candidate of Phys.&Math., Assoc. Professor, Department of Algebra and Geometry, I. Yakovlev Chuvash State Pedagogical University, Cheboksary