Special functions of generalized complex variables in problems of diffraction of elastic shear waves in anisotropic media

We consider the special sk functions of a certain pair of generalized complex variables introduced in the text. These functions form the base functions of particular solutions of the interior and exterior type for the equation describing elastic shear vibrations in an anisotropic medium with a plane of elastic vibrations symmetry. The functions are represented the form of absolutely convergent series and recursion relations, derivative formulas, addition theorems, and asymptotic forms are obtained. Solutions of the metaharmonic equation in cylindrical Bessel functions represent special cases of the solutions constructed here.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 79–83, 1987.