A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i2.4204

Keywords:

confluent hypergeometric limit function, Lerch function, Cauchy integral, Ap\'{e}ry's constant

Keywords:

confluent hypergeometric limit function, Lerch function, Cauchy integral, Ap\'{e}ry's constant

Abstract

A closed form expression of a quadruple integral involving the Hermite polynomial Hn(x) is derived. Special cases are expressed in terms of special functions and fundamental constants. All the results in this work are new.

Author Biographies

Robert Reynolds, York University

Allan Stauffer, York University

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How to Cite

Reynolds, R., & Stauffer, A. . (2022). A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation. European Journal of Pure and Applied Mathematics, 15(2), 620–625. https://doi.org/10.29020/nybg.ejpam.v15i2.4204