Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions
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.
Share and Cite
ISRP Style
S. A. H. Shah, S. Mubeen, Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 2, 109--122
AMA Style
Shah S. A. H., Mubeen S., Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions. J. Nonlinear Sci. Appl. (2022); 15(2):109--122
Chicago/Turabian Style
Shah, S. A. H., Mubeen, S.. "Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions." Journal of Nonlinear Sciences and Applications, 15, no. 2 (2022): 109--122
Keywords
- Meijer \(G\)-functions
- generalized Meijer \(G\)-functions
- Laplace transform
- generalized hypergeometric functions
- generalized Bessel functions
MSC
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