On sharp bounds for ratios of 𝑘-balanced hypergeometric functions

Barnard, Roger; Richards, Kendall; Sliheet, Elyssa

doi:10.1090/proc/14751

On sharp bounds for ratios of $k$-balanced hypergeometric functions
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by Roger W. Barnard, Kendall C. Richards and Elyssa N. Sliheet PDF

Proc. Amer. Math. Soc. 148 (2020), 777-786 Request permission

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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