Concise high precision approximation for the complete elliptic integral of the first kind

DOI10.3934/MATH.2021632OpenAlexW3191523809MaRDI QIDQ2671115

Ling Zhu

Publication date: 3 June 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021632

zbMATH Keywords

rational approximationcomplete elliptic integral of the first kindsimple bounds

Mathematics Subject Classification ID

Means (26E60) Elliptic functions and integrals (33E05)

Related Items (2)

A new upper bound for the complete elliptic integral of the first kind ⋮ Approximations related to the complete \(p\)-elliptic integrals

Cites Work

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• Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
• Inequalities for the Gaussian hypergeometric function
• Asymptotical formulas for Gaussian and generalized hypergeometric functions
• Monotonicity theorems and inequalities for the complete elliptic integrals
• Inequalities for means
• Precise estimates for differences of the Gaussian hypergeometric function
• On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
• Refinements of transformation inequalities for zero-balanced hypergeometric functions
• Sharp bounds for the arithmetic-geometric mean
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Sharp inequalities for the complete elliptic integral of the first kind
• Sharp Estimates for Complete Elliptic Integrals
• Univalence and convexity properties for Gaussian hypergeometric functions

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