A quadruple integral involving the product of generalized parabolic cylinder functions 𝐷ᵥ(𝛽𝑥)𝐷ᵤ(𝛼𝑧): Derivation and evaluation

Proceedings of the American Mathematical Society, Series B Pub Date : 2022-04-18 DOI:10.1090/bproc/126

Robert Reynolds, Allan Stauffer

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Abstract

The aim of the present document is to evaluate a quadruple integral involving the product of the generalized Parabolic Cylinder functions D v ( β x ) D u ( α z ) D_{v}(\beta x)D_{u}(\alpha z) expressed in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.