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Proceedings of the American Mathematical Society

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On sharp bounds for ratios of $ k$-balanced hypergeometric functions


Authors: Roger W. Barnard, Kendall C. Richards and Elyssa N. Sliheet
Journal: Proc. Amer. Math. Soc. 148 (2020), 777-786
MSC (2010): Primary 33C05, 33C75; Secondary 26D15
DOI: https://doi.org/10.1090/proc/14751
Published electronically: August 28, 2019
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Abstract: We extend recently obtained sharp bounds for ratios of zero-balanced hypergeometric functions to the general $ k$-balanced case, $ k\in \mathbb{N}$. We also discuss the absolute monotonicity of generalizations of previously studied functions involving generalized complete elliptic integrals.


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Additional Information

Roger W. Barnard
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Email: Roger.W.Barnard@ttu.edu

Kendall C. Richards
Affiliation: Department of Mathematics, Southwestern University, Georgetown, Texas 78627
Email: richards@southwestern.edu

Elyssa N. Sliheet
Affiliation: Department of Mathematics, Southwestern University, Georgetown, Texas 78627
Email: sliheete@alumni.southwestern.edu

DOI: https://doi.org/10.1090/proc/14751
Keywords: Gaussian hypergeometric function, complete elliptic integrals, generalized complete elliptic integrals.
Received by editor(s): June 9, 2019
Received by editor(s) in revised form: June 10, 2019, and June 20, 2019
Published electronically: August 28, 2019
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society