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...

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Main Authors:	Robert Reynolds, Allan Stauffer
Format:	Article
Language:	English
Published:	AIMS Press 2021-12-01
Series:	AIMS Mathematics
Subjects:	entries of gradshteyn and ryzhik hyperbolic integrals hypergeometric function lerch function
Online Access:	http://www.aimspress.com/article/doi/10.3934/math.2021109http://www.aimspress.com/article/doi/10.3934/math.2021109

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spelling	doaj-07f477c621d546a6936a0d50fb3bd0852020-12-16T01:48:02ZengAIMS PressAIMS Mathematics2473-69882021-12-01621816182110.3934/math.2021109Derivation of some integrals in Gradshteyn and RyzhikRobert Reynolds0Allan Stauffer1Department of Mathematics, York University, 4700 Keele Street, Toronto, M3J1P3, CanadaDepartment of Mathematics, York University, 4700 Keele Street, Toronto, M3J1P3, Canada 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.http://www.aimspress.com/article/doi/10.3934/math.2021109http://www.aimspress.com/article/doi/10.3934/math.2021109entries of gradshteyn and ryzhikhyperbolic integralshypergeometric functionlerch function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Robert Reynolds Allan Stauffer
spellingShingle	Robert Reynolds Allan Stauffer Derivation of some integrals in Gradshteyn and Ryzhik AIMS Mathematics entries of gradshteyn and ryzhik hyperbolic integrals hypergeometric function lerch function
author_facet	Robert Reynolds Allan Stauffer
author_sort	Robert Reynolds
title	Derivation of some integrals in Gradshteyn and Ryzhik
title_short	Derivation of some integrals in Gradshteyn and Ryzhik
title_full	Derivation of some integrals in Gradshteyn and Ryzhik
title_fullStr	Derivation of some integrals in Gradshteyn and Ryzhik
title_full_unstemmed	Derivation of some integrals in Gradshteyn and Ryzhik
title_sort	derivation of some integrals in gradshteyn and ryzhik
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2021-12-01
description	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.
topic	entries of gradshteyn and ryzhik hyperbolic integrals hypergeometric function lerch function
url	http://www.aimspress.com/article/doi/10.3934/math.2021109http://www.aimspress.com/article/doi/10.3934/math.2021109
work_keys_str_mv	AT robertreynolds derivationofsomeintegralsingradshteynandryzhik AT allanstauffer derivationofsomeintegralsingradshteynandryzhik
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Derivation of some integrals in Gradshteyn and Ryzhik

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