A Triple Integral Containing the Lommel Function su,v(z): Derivation and Evaluation

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4282

Keywords:

Lommel Function, Triple integral, Catalan's constant, Cauchy integral

Abstract

A three-dimensional integral containing the kernel g(x, y, z)su,v(z) is derived. The function g(x, y, z) is a generalized function containing the logarithmic and exponential functions and su,v(z) is the Lommel function and the integral is taken over the cube 0 ≤ y ≤ ∞, 0 ≤ x ≤∞, 0 ≤ z ≤ ∞. A representation in terms of the Lerch function is derived, from which special cases can be evaluated. Almost all Hurwitz-Lerch Zeta functions have an asymmetrical zero distribution. All the results in this work are new.

Author Biography

Robert Reynolds, York University

I enjoy, reading, walking, playing tennis. I practise mathemtics in my spare time.

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Published

2022-07-31

How to Cite

Reynolds, R., & Stauffer, A. . (2022). A Triple Integral Containing the Lommel Function su,v(z): Derivation and Evaluation. European Journal of Pure and Applied Mathematics, 15(3), 992–998. https://doi.org/10.29020/nybg.ejpam.v15i3.4282

Issue

Vol. 15 No. 3: (July 2022)

Section

Nonlinear Analysis

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Copyright (c) 2022 European Journal of Pure and Applied Mathematics

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