Convergence of power series in the method of initial functions

An algorithm for constructing basic equations of the method initial functions (MIF) for plane problems of elasticity theory for anisotropic solids in an orthogonal Cartesian coordinate system in matrix-operator form using a general solution of elasticity theory equations in displacements through two arbitrary functions is presented. Displacements and stresses at an arbitrary point of an elastic body are obtained as a result of an impact of MIF operators to displacements and stresses (initial functions) defined on a coordinate line. The MIF operators are obtained in the form of power operator series in which the operator acts as a differentiation operator with respect to one of the independent variables. Regularity of MIF operators for an arbitrary anisotropic body is shown. Convergence of power series in the MIF solution in the case of the initial functions definition in terms of trigonometric sines and cosines is proved.