Integral transforms involving the product of Humbert and Bessel functions and its application

A. Belafhal; N. Nossir; L. Dalil-Essakali; T. Usman; A. Belafhal; N. Nossir; L. Dalil-Essakali; T. Usman

doi:10.3934/math.2020086

AIMS Mathematics

2020, Volume 5, Issue 2: 1260-1274. doi: 10.3934/math.2020086

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Research article

Integral transforms involving the product of Humbert and Bessel functions and its application

1.
LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, P. B 20, 24000 El Jadida, Morocco
2.
Department of Mathematics, School of Basic and Applied Sciences, Lingaya’s Vidyapeeth, Faridabad-121002, Haryana, India

Received: 10 October 2019 Accepted: 06 January 2020 Published: 19 January 2020
MSC : 33B15, 33C10, 33C15

In this paper, we develop some integral transforms involving a product of Humbert and Bessel functions with a weight e^-γx². These integral transforms will be evaluated in terms of hypergeometric functions. Various transformation formulae are also evaluated in terms of Appell functions to complete this study. Some special cases of the evaluated integrals yield some infinite series of generalized hypergeometric and Appell functions. As application, one of our main results is investigated to give an expression of the Generalized Humbert-Gaussian beams (GHGBs) propagating through a paraxial ABCD optical system.
- integral transforms,
- Bessel functions,
- Humbert functions,
- Appell functions,
- Hypergeometric functions
Citation: A. Belafhal, N. Nossir, L. Dalil-Essakali, T. Usman. Integral transforms involving the product of Humbert and Bessel functions and its application[J]. AIMS Mathematics, 2020, 5(2): 1260-1274. doi: 10.3934/math.2020086

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Abstract

In this paper, we develop some integral transforms involving a product of Humbert and Bessel functions with a weight e^-γx². These integral transforms will be evaluated in terms of hypergeometric functions. Various transformation formulae are also evaluated in terms of Appell functions to complete this study. Some special cases of the evaluated integrals yield some infinite series of generalized hypergeometric and Appell functions. As application, one of our main results is investigated to give an expression of the Generalized Humbert-Gaussian beams (GHGBs) propagating through a paraxial ABCD optical system.

References

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