Particular Solutions of Multidimensional Generalized Euler-Poisson-Darboux Equations of Elliptic or Hyperbolic Types

The main result of the present paper is the construction of particular solutions for a class ofmultidimensional partial differential equations with several singular coefficients of second order.These particular solutions are directly connected with the first Lauricella's hypergeometricfunction. The expansion formula is required for particular solutions investigation which wouldexpress the first Lauricella function in terms of products of several simpler hypergeometricfunctions involving fewer variables. In this paper, the singularity order at the origin and otherproperties of the particular solutions are determined.