Hypergeometric functions and hyperbolic metric

DOI10.1007/BF03321727zbMath1161.30030arXiv0805.1501OpenAlexW2044311467MaRDI QIDQ2378582

Toshiyuki Sugawa, Glenn D. Anderson, Mavina K. Vamanamurthy, Matti Vuorinen

Publication date: 13 January 2009

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.1501

zbMATH Keywords

convexityhypergeometric functionshyperbolic metriccomplete elliptic integralsPoincaré densitySugawa-Vuorinen conjecture

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Cites Work

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• Turán type inequalities for generalized complete elliptic integrals
• Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral
• Mapping properties of hypergeometric functions and convolutions of starlike or convex functions of order \(\alpha\)
• Generalized elliptic integrals
• Generalized elliptic integrals and the Legendre \(\mathcal M\)-function
• Estimation of the hyperbolic metric by using the punctured plane
• Some inequalities for the Poincaré metric of plane domains
• Generalized convexity and inequalities
• The Poincaré Metric on the Twice Punctured Plane and the Theorems of Landau and Schottky
• Precise Bounds in the Theorems of Schottky and Picard
• The Poincaré Metric of Plane Domains
• Asymptotic expansions and inequalities for hypergeometric function
• Comparing Poincaré densities

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