A note on inequalities for the ratio of zero-balanced hypergeometric functions

DOI10.1090/bproc/41zbMath1414.33007OpenAlexW2944272124WikidataQ127915083 ScholiaQ127915083MaRDI QIDQ5377084

Kendall C. Richards

Publication date: 23 May 2019

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bproc/41

zbMATH Keywords

Gaussian hypergeometric functioncomplete elliptic integralzero-balanced hypergeometric function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (9)

On some refinements for inequalities involving zero-balanced hypergeometric function ⋮ Absolute monotonicity involving the complete elliptic integrals of the first kind with applications ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ On the absolute monotonicity of generalized elliptic integral of the first kind ⋮ Monotonicity and convexity involving generalized elliptic integral of the first kind ⋮ Absolutely monotonic functions involving the complete elliptic integrals of the first kind with applications ⋮ A concavity property of generalized complete elliptic integrals ⋮ On sharp bounds for ratios of 𝑘-balanced hypergeometric functions ⋮ On the convexity and concavity of generalized complete elliptic integral of the first kind

Uses Software

• DLMF

Cites Work

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• Turán type inequalities for generalized complete elliptic integrals
• Generalized elliptic integrals and modular equations
• An inequality for generalized complete elliptic integral
• On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
• Monotonicity properties and inequalities for the generalized elliptic integral of the first kind
• A note on the hypergeometric mean value
• Inequalities for the ratio of complete elliptic integrals
• Functional Inequalities for Complete Elliptic Integrals and Their Ratios
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Inequalities for Zero-Balanced Hypergeometric Functions

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