A Triple Integral Containing the Lommel Function su,v(z): Derivation and Evaluation
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Published:2022-07-31
Issue:3
Volume:15
Page:992-998
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ISSN:1307-5543
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Container-title:European Journal of Pure and Applied Mathematics
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language:
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Short-container-title:Eur. J. Pure Appl. Math.
Author:
Reynolds RobertORCID,
Stauffer Allan
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.
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science