Open AccessA quintuple integral involving the product of Hermite polynomial $ H_{n}(\beta x) $ and parabolic cylinder function $ D_{v}(\alpha t) $: derivation and evaluation
Author(s) -
Robert Reynolds,
AUTHOR_ID,
A D Stauffer
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022418
Subject(s) - hermite polynomials , beta (programming language) , mathematics , product (mathematics) , cylinder , function (biology) , parabolic cylinder function , polynomial , alpha (finance) , integral transform , mathematical analysis , geometry , differential equation , parabolic partial differential equation , construct validity , statistics , evolutionary biology , computer science , biology , programming language , psychometrics
In this paper, we derive an integral transform involving the product of Hermite polynomial $ H_{n}(\beta x) $ and parabolic cylinder function $ D_{v}(\alpha 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.