PARTICULAR SOLUTIONS OF MULTIDIMENSIONAL GENERALIZED EULER-POISSON-DARBOUX EQUATIONS OF ELLIPTIC OR HYPERBOLIC TYPE
Ryskan A.R. Arzikulov Z.O. Ergashev T.G.
9 April 2024al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2024#121Issue 176 - 88 pp.
The main result of the present paper is the construction of particular solutions for a class of multidimensional partial differential equations with several singular coefficients of second order. These particular solutions are directly connected with the first Lauricella’s hypergeometric function. The expansion formula is required for particular solutions investigation which would express the first Lauricella function in terms of products of several simpler hypergeometric functions involving fewer variables. In this paper, the singularity order at the origin and other properties of the particular solutions are determined.
expansion formula , Lauricella’s hypergeometric function , multidimensional generalized Euler-Poisson-Darboux equation , order of the singularity , particular solutions
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Abai Kazakh National Pedagogical University, Almaty, Kazakhstan
Narxoz University, Almaty, Kazakhstan
Fergana Polytechnic Institute, Fergana, Uzbekistan
TIIAME National Research University, Tashkent, Uzbekistan
Ghent University, Ghent, Belgium
Abai Kazakh National Pedagogical University
Narxoz University
Fergana Polytechnic Institute
TIIAME National Research University
Ghent University
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