Work

On Some Formulas for the Lauricella Function

Year: 2023

Type: article

Abstract: 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.

Source: Mathematics

DOI: 10.3390/math11244978

Authors: Ainur Ryskan, Tuhtasin Ergashev

Institutions: Abai Kazakh National Pedagogical University, Ghent University, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,336

Funder: Ministry of Education and Science of the Republic of Kazakhstan