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Inequalities for some integrals involving modified Bessel functions


Author: Robert E. Gaunt
Journal: Proc. Amer. Math. Soc. 147 (2019), 2937-2951
MSC (2010): Primary 33C10, 26D15
DOI: https://doi.org/10.1090/proc/14433
Published electronically: March 5, 2019
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Abstract: Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double inequality, involving the modified Bessel function of the first kind, for a generalized hypergeometric function. We also present some open problems that arise from this research.


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Additional Information

Robert E. Gaunt
Affiliation: School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
Email: robert.gaunt@manchester.ac.uk

DOI: https://doi.org/10.1090/proc/14433
Received by editor(s): June 1, 2018
Received by editor(s) in revised form: October 5, 2018
Published electronically: March 5, 2019
Additional Notes: The author was supported by a Dame Kathleen Ollerenshaw Research Fellowship.
Communicated by: Yuan Xu
Article copyright: © Copyright 2019 American Mathematical Society