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Results in Mathematics

, 74:57 | Cite as

Inequalities for Integrals of the Modified Struve Function of the First Kind II

  • Robert E. GauntEmail author
Open Access
Article

Abstract

Simple inequalities are established for integrals of the type \(\int _0^x \mathrm {e}^{-\gamma t} t^{-\nu } \mathbf {L}_\nu (t)\,\mathrm {d}t\), where \(x>0\), \(0\le \gamma <1\), \(\nu >-\frac{3}{2}\) and \(\mathbf {L}_{\nu }(x)\) is the modified Struve function of the first kind. In most cases, these inequalities are tight in certain limits. As a consequence we deduce a tight double inequality, involving the modified Struve function \(\mathbf {L}_{\nu }(x)\), for a generalized hypergeometric function.

Keywords

Modified Struve function inequality integral 

Mathematics Subject Classification

Primary 33C10 26D15 

Notes

Acknowledgements

The author is supported by a Dame Kathleen Ollerenshaw Research Fellowship.

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Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of MathematicsThe University of ManchesterManchesterUK

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