Generalized elliptic integrals and the Legendre \(\mathcal M\)-function
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Publication:2473878
DOI10.1016/j.jmaa.2007.05.020zbMath1135.33008arXivmath/0701438OpenAlexW2125240734MaRDI QIDQ2473878
Ville Heikkala, Henri Lindén, Mavina K. Vamanamurthy, Matti Vuorinen
Publication date: 5 March 2008
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0701438
Related Items (27)
On generalized complete elliptic integrals and modular functions ⋮ Monotonicity and functional inequalities for the complete \(p\)-elliptic integrals ⋮ Generalized elliptic integrals ⋮ Hypergeometric functions and hyperbolic metric ⋮ On generalized complete \((p, q)\)-elliptic integrals ⋮ Topics in Special Functions III ⋮ On the generalized modulus ⋮ Monotonicity, convexity, and inequalities for the generalized elliptic integrals ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind ⋮ Discrete approximation of complete \(p\)-elliptic integral of the second kind and its application ⋮ Generalized Hersch-Pfluger distortion function and complete elliptic integrals ⋮ Inequalities for the generalized elliptic integrals with respect to Hölder means ⋮ A sharp lower bound for the complete elliptic integrals of the first kind ⋮ Sharp inequalities for the generalized elliptic integrals of the first kind ⋮ Solution to a conjecture on the Legendre \(M\)-function with an application to the generalized modulus ⋮ Monotonicity properties and bounds for the complete \(p\)-elliptic integrals ⋮ Inequalities and bounds for generalized complete elliptic integrals ⋮ Topics in special functions. II ⋮ Convexity and concavity of the complete elliptic integrals with respect to Lehmer mean ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function ⋮ Functional inequalities for the ratio of complete \(p\)-elliptic integrals ⋮ Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function ⋮ Precise bounds for the weighted Hölder mean of the complete \(p\)-elliptic integrals ⋮ A survey for generalized trigonometric and hyperbolic functions ⋮ Sharp bounds for generalized elliptic integrals of the first kind ⋮ Convexity and monotonicity for elliptic integrals of the first kind and applications
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- Generalized elliptic integrals and modular equations
- Generalized convexity and inequalities
- Ramanujan and hypergeometric and basic hypergeometric series
- Monotonicity Rules in Calculus
- Ramanujan's Theories of Elliptic Functions to Alternative Bases
- Duplication inequalities for the ratios of hypergeometric functions
- Generating Functions for Bessel and Related Polynomials
- On hypergeometric functions and generalizations of Legendre's relation
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