A QUADRUPLE INTEGRAL INVOLVING THE EXPONENTIAL LOGARITHM OF QUOTIENT RADICALS IN TERMS OF THE HURWITZ-LERCH ZETA FUNCTION

Robert Reynolds     (Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada)
Allan Stauffer     (Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada)

Abstract


With a possible connection to integrals used in General Relativity, we used our contour integral method  to write a closed form solution for a quadruple integral involving exponential functions and  logarithm of quotient radicals. Almost all Hurwitz–Lerch Zeta functions have an asymmetrical zero distribution. All the results in this work are new.


Keywords


Quadruple integral, Hurwitz-Lerch zeta function, Catalan's constant, Cauchy integral, Glaisher's constant

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DOI: http://dx.doi.org/10.15826/umj.2022.2.013

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