Some Novel Laplace-Transform Based Integrals via Hypergeometric Techniques

Authors

H. M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada\\Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China\\Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, AzerbaijanFollow
M. I. Qureshi, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, IndiaFollow
Showkat Ahmad Dar, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, IndiaFollow

Author Country (or Countries)

India

Abstract

In this paper, we investigate and evaluate a number of novel Laplace-transform based integrals under suitable convergence conditions. In our derivations, we make use of the hypergeometric approach involving algebraic properties of the Pochhammer symbol and classical summation theorems of the hypergeometric series 2F1(1), 2F1(−1) and 4F3(−1). We also obtain the Laplace transforms of arbitrary powers of some finite series, which contain the hyperbolic sine and cosine functions with different arguments, in terms of the hypergeometric and Beta functions. Moreover, we derive the Laplace transforms of the even and odd positive integer powers of the trigonometric sine and cosine functions with different arguments, as well as their combinations in products involving two, three or four functions at a time. Finally, several interesting special cases of the main results are considered.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140501

Recommended Citation

M. Srivastava, H.; I. Qureshi, M.; and Ahmad Dar, Showkat (2020) "Some Novel Laplace-Transform Based Integrals via Hypergeometric Techniques," Applied Mathematics & Information Sciences: Vol. 14: Iss. 5, Article 1.
DOI: http://dx.doi.org/10.18576/amis/140501
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss5/1