Sharp power mean bounds for the Gaussian hypergeometric function

DOI10.1016/j.jmaa.2005.01.018zbMath1065.33005OpenAlexW2005630774MaRDI QIDQ557878

Kendall C. Richards

Publication date: 30 June 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.01.018

zbMATH Keywords

Elliptic integralHypergeometric functionPower mean

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (18)

Contiguous relations and their computations for \(_2F_1\) hypergeometric series ⋮ Topics in Special Functions III ⋮ Optimal combinations bounds of root-square and arithmetic means for Toader mean ⋮ On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving the Finslerian length of tangent vectors ⋮ Contiguous relations for \(_{2}F_{1}\) hypergeometric series ⋮ Sharp approximations for complete \(p\)-elliptic integral of the second kind by weighted power means ⋮ An introduction to the theory of generalized conics and their applications ⋮ Concavity of the complete elliptic integrals of the second kind with respect to Hölder means ⋮ On Euler products with smaller than one exponents ⋮ Inequalities between arithmetic-geometric, Gini, and Toader means ⋮ Convexity of the complete elliptic integrals of the first kind with respect to Hölder means ⋮ A power mean inequality involving the complete elliptic integrals ⋮ Inequalities and bounds for a certain bivariate elliptic mean II ⋮ Two sharp inequalities for power mean, geometric mean, and harmonic mean ⋮ Optimal power mean bounds for the weighted geometric mean of classical means ⋮ Optimal inequalities among various means of two arguments ⋮ On some new contiguous relations for the Gauss hypergeometric function with applications ⋮ Inequalities and bounds for generalized complete elliptic integrals

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• Monotonicity theorems and inequalities for the complete elliptic integrals
• Inequalities for compound mean iterations with logarithmic asymptotes
• A note on the hypergeometric mean value
• Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
• A Monotonicity Property Involving ₃F₂ and Comparisons of the Classical Approximations of Elliptical Arc Length
• An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse
• Some Inequalities for Hypergeometric Functions

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