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Research Article | Open Access

A quintuple integral involving the product of Hermite polynomial H n ( β x ) and parabolic cylinder function D v ( α t ): derivation and evaluation

Robert Reynolds( ), Allan Stauffer
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, M3J1P3, Canada
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Abstract

In this paper, we derive an integral transform involving the product of Hermite polynomial H n ( β x ) and parabolic cylinder function D v ( α t ). These integral transforms will be evaluated in terms of Lerch function. Various formulae are also evaluated in terms of special functions to complete this paper. All the results in this paper are new.

Keywords

parabolic cylinder functionquintuple integralLerch functionCauchy integral
CLC number: 30E20, 33-01, 33-03, 33-04, 33-33B

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7464-7470
DOI: 10.3934/math.2022418

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Reynolds R, Stauffer A. A quintuple integral involving the product of Hermite polynomial H n ( β x ) and parabolic cylinder function D v ( α t ): derivation and evaluation. AIMS Mathematics, 2022, 7(5): 7464-7470. https://doi.org/10.3934/math.2022418

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Received: 15 December 2021
Revised: 21 January 2022
Accepted: 25 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)