On Some Formulas for the Lauricella Function

Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. 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...

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Vydáno v:Mathematics (Basel) Ročník 11; číslo 24; s. 4978
Hlavní autoři: Ryskan, Ainur, Ergashev, Tuhtasin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.12.2023
Témata:
Analysis
Appell functions
Boundary value problems
Decomposition
differentiation formulas
Equality
expansion formulas
Formulae
Functions, Hypergeometric
Hypergeometric functions
integral representation
Lauricella functions
Mathematical analysis
Mathematics
Parameters
Partial differential equations
Representations
summation formulas
Variables
Variables (Mathematics)
Kazakhstan
ISSN:2227-7390, 2227-7390
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Shrnutí:Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. 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 FA(n), 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 FA(n) function, definitions of gamma and beta functions, and the Gaussian hypergeometric function of one variable are used.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11244978