# Article ID: MTJPAM-D-20-00016

## Title: Some Hypergeometric Summation Theorems and Reduction Formulas via Laplace Transform Method

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

Article ID: MTJPAM-D-20-00016; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 182-199

Document Type: Research Paper

Author(s): Mohammad Idris Qureshi a , Showkat Ahmad Dar b

aDepartment of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (Central University), New Delhi, 110025, India

bDepartment of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (Central University), New Delhi, 110025, India — Post Graduate Department of Mathematics, Govt. Degree College Boys Baramulla, University of Kashmir, Kashmir, 193502, India

Received: 29 June 2020, Accepted: 4 September 2020, Published: 25 April 2021.

Corresponding Author: Showkat Ahmad Dar (Email address: showkatjmi134@gmail.com)

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Abstract

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions 3F2(±1), 4F3(±1), 5F4(±1), 6F5(±1), 7F6(±1) and 8F7(±1) with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for 4F3(1), 7F6(−1) and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for 3F2(−1),6F5(±1), 7F6(±1) and 8F7(±1) are obtained.

Keywords: Generalized hypergeometric functions, Summation and multiplication theorems, Laplace transform, Beta and Gamma function

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