The paper presents some basic points of the theory of expansions in Papkovich–Fadle eigenfunctions in the polar coordinate system. Formulas for the Papkovich–Fadle eigenfunctions corresponding to the boundary value problem of the theory of elasticity for a truncated wedge with free long sides are given. Equations for determining the functions biorthogonal to the Papkovich–Fadle functions are constructed. Examples of expansions into Lagrange series, which are the basis for solving boundary value problems, are given.
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