Complete (p,q)-elliptic integrals with application to a family of means

DOI10.7153/JCA-10-02zbMath1424.33033arXiv1507.01383OpenAlexW1694286200MaRDI QIDQ4627826

Toshiki Kamiya, Shingo Takeuchi

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01383

zbMATH Keywords

logarithmic mean\(p\)-Laplaciancomplete elliptic integralsGaussian hypergeometric functionsarithmetic-geometric meangeneralized trigonometric functions

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (16)

The inverse hyperbolic tangent function and Jacobian sine function ⋮ On generalized complete \((p, q)\)-elliptic integrals ⋮ Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers ⋮ Generalized elliptic integrals and generalized Grötzsch function with two parameters ⋮ Inequalities and bounds for the \(p\)-generalized trigonometric functions ⋮ Fractional integral inequalities for generalized-\(\mathbf{m}\)-\(((h_1^p,h_2^q); (\eta_1,\eta_2))\)-convex mappings via an extended generalized Mittag-Leffler function ⋮ Sharp exponential type inequalities for the arc lemniscate sine function with applications ⋮ Monotonicity and sharp inequalities related to complete \((p,q)\)-elliptic integrals of the first kind ⋮ Applications of generalized trigonometric functions with two parameters ⋮ Monotonicity properties and bounds for the complete \(p\)-elliptic integrals ⋮ Monotonicity properties and inequalities for the generalized elliptic integral of the first kind ⋮ On a function involving generalized complete \((p, q)\)-elliptic integrals ⋮ Monotonicity and inequalities related to the generalized inverse lemniscate functions ⋮ Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function ⋮ Functional inequalities for generalized complete elliptic integrals with two parameters ⋮ A survey for generalized trigonometric and hyperbolic functions

Cites Work

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• A new form of the generalized complete elliptic integrals
• The basis property of generalized Jacobian elliptic functions
• Eigenvalues, embeddings and generalised trigonometric functions
• Generalized Jacobian elliptic functions and their application to bifurcation problems associated with \(p\)-Laplacian
• Some remarkable sine and cosine functions
• On the closed solution to some nonhomogeneous eigenvalue problem with \(p\)-Laplacian
• Legendre-type relations for generalized complete elliptic integrals
• Inequalities for the generalized trigonometric and hyperbolic functions with two parameters

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