Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation

In this article, a new inverse pair of symbolic operators with the multidimensional analogues is introduced. The properties of inverse pair of symbolic operators with the multidimensional analogues are studied. Formulas for the infinite expansion of multiple Lauricella functions are established. The application of some expansions in studying the properties of fundamental solutions of singular elliptic equations is shown.

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