On some properties of exact solutions in the form of series in Papkovich–Fadle eigenfunctions

In solving boundary value problems of elasticity theory in a half-strip in the form of series in Papkovich–Fadle eigenfunctions, there are always two representations for these functions. In the paper we consider Lagrange expansions in these representations. Lagrange expansions are the expansions of only one function in a series in any single system of Papkovich–Fadle eigenfunctions. This is different from the expansions that arise in solving boundary value problems where it is necessary to construct the expansions of two functions (given at the end of the half-strip) with one set of coefficients. Lagrange expansions play a fundamental role in solving boundary value problems with different boundary conditions on the long sides of the half-strip, similar to the one that trigonometric series play in periodic problems of the theory of elasticity.