This article is cited in 1 paper

Mathematics and Mechanics

On the Mellin–Barnes integral representation of one special function

F. G. Khushtova

Institute of Applied Mathematics and Automation – branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 360000, Russia, Nalchik, 89 A Shortanov street

Abstract: The paper considers the Mellin–Barnes integral representation of a special function that arises in the theory of boundary value problems for parabolic equations with a Bessel operator and a fractional time derivative. The convergence of such an integral is investigated. The expansion of the considered function into power series and asymptotic formulas for large and small values of the argument is given. For particular values of the parameters of the function under consideration, some well-known elementary and special functions are obtained.

Keywords: Mellin–Barnes integral, hypergeometric function, gamma function.

UDC: 517.58

MSC: Primary 33C60; Secondary 33E50

Received: 01.12.2022
Revised: 12.12.2022
Accepted: 15.12.2022

DOI: 10.35330/1991-6639-2022-6-110-19-27

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