Article ID: MTJPAM-D-20-00048

Title: Integrals with Two–Variable Generating Function in the Integrand


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00048; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 95-103

Document Type: Research Paper

Author(s): Musharraf Ali a , Mohd Ghayasuddin b , Tibor K. Pogány c

aDepartment of Mathematics, G.F. College, Shahjahanpur-242001, India

bDepartment of Mathematics, Integral University Campus, Shahjahanpur-242001, India

cFaculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia and Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary

Received: 17 December 2020, Accepted: 30 December 2020, Published: 25 April 2021.

Corresponding Author: Tibor K. Pogány (Email addresses: poganj@pfri.hr; pogany.tibor@uni-obuda.hu)

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Abstract

The main motive of this study is to present a new class of generalized integral formulae which involve a generating function of two variables G(u, x). By this approach we deduce a set of new outcomes, which are integrals associated with generalized hypergeometric function, Laguerre, Hermite and Bessel polynomials, Kampé de Fériet hypergeometric series of two variables, Lauricella function and several special cases of our main results.

Keywords: Generating functions, Lauricella hypergeometric function FD(m), Appell–Horn hypergeometric function F1 of two variables, Kampé de Fériet series, Hypergeometric functions, Generalized Bessel polynomials, Hermite polynomials

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