A survey of some bounds for Gauss' hypergeometric function and related bivariate means

Roger Barnard, Kendall C. Richards, Hilari C. Tiedeman

Type: Article

Publication Date: 2010-01-01

Citations: 10

DOI: https://doi.org/10.7153/jmi-04-06

Abstract

We give an expository summary of a collection of inequalities involving Gauss' hypergeometric function 2 F 1 and the closely-related power mean (and certain other bivariate means).Two conjectures involving simultaneous sharp bounds for the hypergeometric function are included.Sharpness for the corresponding zero-balanced case is observed.

Locations

Journal of Mathematical Inequalities - View - PDF

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+	Inequalities for Means	1994	M. K. Vamanamurthy Матти Вуоринен
+ PDF Chat	An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse	2000	Roger Barnard Kent Pearce Kendall C. Richards
+	Hypergeometric analogues of the arithmetic-geometric mean iteration	1993	Jonathan M. Borwein Peter Borwein Frank G. Garvan
+	Sharp power mean bounds for the Gaussian hypergeometric function	2005	Kendall C. Richards
+ PDF Chat	Inequalities for zero-balanced hypergeometric functions	1995	G. D. Anderson Roger Barnard Kendall C. Richards M. K. Vamanamurthy Матти Вуоринен
+	Inequalities and bounds for elliptic integrals	2007	Haseeb Kazi Edward Neuman
+	Inequalities for Compound Mean Iterations with Logarithmic Asymptotes	1993	Jonathan M. Borwein Peter Borwein
+ PDF Chat	Some inequalities for hypergeometric functions	1966	B. C. Carlson
+	Inequalities for differences of powers	1988	Zsolt Páles
+	Hypergeometric functions in the geometric function theory	2006	T. N. Shanmugam