June 2021 Some identities for Mellin, Kontorovich-Lebedev transforms with applications
Arman Aghili
Tbilisi Math. J. 14(2): 239-253 (June 2021). DOI: 10.32513/tmj/19322008136

Abstract

In this article, the author used Mellin and Kontorovich-Lebedev transforms to establish certain integrals involving Macdonald's functions. Transform method is a powerful tool for solving singular integral equations, evaluation of certain integrals and solution to partial differential equations. The result reveals that the transform method is very convenient and effective.

Funding Statement

The author is partially supported by the university of Guilan.

Acknowledgment

The author would like to express his sincere thanks to the editor/s and referee for careful reading of the manuscript and helpful suggestions that leads to the vast improvement of the paper.

Citation

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Arman Aghili. "Some identities for Mellin, Kontorovich-Lebedev transforms with applications." Tbilisi Math. J. 14 (2) 239 - 253, June 2021. https://doi.org/10.32513/tmj/19322008136

Information

Received: 16 September 2020; Accepted: 20 February 2021; Published: June 2021
First available in Project Euclid: 2 July 2021

MathSciNet: MR4298946
zbMATH: 1493.30081
Digital Object Identifier: 10.32513/tmj/19322008136

Subjects:
Primary: 65R10
Secondary: 30E20 , 33C10 , 33C47

Keywords: Airy function , associated Legendre function , Bessel function , conical function , Kontorovich-Lebedev transform , Macdonald's function , Mellin transform , Schlomilch integral equation

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 2 • June 2021
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