Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions

Volume 15, Issue 2, pp 109--122 http://dx.doi.org/10.22436/jnsa.015.02.03

Publication Date: September 17, 2021 Submission Date: June 09, 2021 Revision Date: July 16, 2021 Accteptance Date: July 26, 2021

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Authors

S. A. H. Shah - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. S. Mubeen - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Abstract

The aim of this paper is to prove Laplace transform of some special functions in term of generalized Meijer \(G\)-functions. Some properties of generalized Meijer \(G\)-functions will be discussed. We investigate the Laplace transform of different hypergeometric functions in the form of generalized Meijer \(G\)-functions and hypergeometric functions. We derive Laplace transform of Bessel \(k\)-functions, hyper-Bessel \(k\)-functions, incomplete gamma \(k\)-function, sine \(k\)-integral, sine hyperbolic \(k\)-integral, Kelvin \(k\)-function in the form of generalized Meijer \(G\)-functions. In fact, we provide new approach to find Laplace transform of said functions.

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Keywords

• Meijer \(G\)-functions
• generalized Meijer \(G\)-functions
• Laplace transform
• generalized hypergeometric functions
• generalized Bessel functions

MSC

•  33C60
•  44A10
•  33C20
•  33C10

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