On Some Formulas for the Lauricella Function

Ryskan A. Ergashev T.
December 2023 Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2023 #11 Issue 24

Lauricella, G. in 1893 defined four multidimensional hypergeometric functions (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.). These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of variables and corresponding parameters, each of them has its own parameters. In the present work for Lauricella’s function (Formula presented.), the limit formulas are established, some expansion formulas are obtained that are used to write recurrence relations, and new integral representations and a number of differentiation formulas are obtained that are used to obtain the finite and infinite sums. In the presentation and proof of the obtained formulas, already known expansions and integral representations of the considered (Formula presented.) function, definitions of gamma and beta functions, and the Gaussian hypergeometric function of one variable are used.

Appell functions , differentiation formulas , expansion formulas , integral representation , Lauricella functions , summation formulas

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Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, 86 Tole Bi Street, Almaty, 050012, Kazakhstan
Department of Higher Mathematics, National Research University “TIIAME”, 39 Kari-Niyazi Street, Tashkent, 100000, Uzbekistan
Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Gent, 9000, Belgium

Institute of Mathematics
Department of Higher Mathematics
Department of Mathematics

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