Decomposition formulas for some quadruple hypergeometric series
Abdumauvlen BerdyshevAbai Kazakh National Pedagogical University, Almaty, Kazakhstan;Anvar HasanovInstitute of mathematics, Uzbek academy of sciences, Tashkent, Uzbekistan;Айнур РысканAbai Kazakh National Pedagogical University, Almaty, Kazakhstan;
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In the present work, the authors obtained operator identities and decomposition formulas for second order Gauss hypergeometric series of four variables into products containing simpler hypergeometric functions. A Choi–Hasanov method based on the inverse pairs of symbolic operators is used. The obtained expansion formulas for the hypergeometric functions of four variables will allow us to study the properties of these functions. These decompositions are used to study the solvability of boundary value problems for degenerate multidimensional partial differential equations.
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