Derivation of some integrals in Gradshteyn and Ryzhik

In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the formandin terms of the Lerch function where $ k $, $ a $, $ z $ and $ b $ are arbitrary complex numbers. The ent...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 2; pp. 1816 - 1821
Main Authors Reynolds, Robert, Stauffer, Allan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
entries of gradshteyn and ryzhik
hyperbolic integrals
hypergeometric function
lerch function
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021109

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Summary:In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the formandin terms of the Lerch function where $ k $, $ a $, $ z $ and $ b $ are arbitrary complex numbers. The entries in the table(s) are obtained as special cases in the paper below.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021109