Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
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Publication:4561095
DOI10.7153/mia-2018-21-82zbMath1403.33012OpenAlexW2898226816WikidataQ129049092 ScholiaQ129049092MaRDI QIDQ4561095
Wei-Mao Qian, Zhen-Hang Yang, Yu-Ming Chu
Publication date: 10 December 2018
Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.7153/mia-2018-21-82
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Uses Software
Cites Work
- Accurate approximations for the complete elliptic integral of the second kind
- Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
- Optimal combinations bounds of root-square and arithmetic means for Toader mean
- Sharp inequalities involving the power mean and complete elliptic integral of the first kind
- Concavity of the complete elliptic integrals of the second kind with respect to Hölder means
- Bounds for complete elliptic integrals of the second kind with applications
- A power mean inequality involving the complete elliptic integrals
- On the modulus of the Grötzsch ring
- Two optimal double inequalities between power mean and logarithmic mean
- A class of logarithmically completely monotonic functions associated with a gamma function
- Sharp generalized Seiffert mean bounds for Toader mean
- The Schur convexity of Gini mean values in the sense of harmonic mean
- Asymptotic formulas for gamma function with applications
- Asymptotical formulas for Gaussian and generalized hypergeometric functions
- Some properties for a class of symmetric functions with applications
- Monotonicity theorems and inequalities for the complete elliptic integrals
- The Schur harmonic convexity for a class of symmetric functions
- The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications
- Ostrowski type inequalities involving conformable fractional integrals
- Optimal lower and upper bounds for the geometric convex combination of the error function
- Necessary and sufficient conditions such that extended mean values are Schur-convex or Schur-convave
- Schur-convexity for a class of symmetric functions and its applications
- Two sharp inequalities for power mean, geometric mean, and harmonic mean
- Inequalities for generalized logarithmic means
- Schur convexity for a class of symmetric functions
- Bounds for the ratio of two gamma functions
- The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means
- Convexity with respect to Hölder mean involving zero-balanced hypergeometric functions
- Monotonic and logarithmically convex properties of a function involving gamma functions
- The Schur harmonic convexity of the Hamy symmetric function and its applications
- Solution of an open problem for Schur convexity or concavity of the Gini mean values
- Generalized elliptic integrals and modular equations
- Inequalities for means
- Some mean values related to the arithmetic-geometric mean
- Elliptic integral inequalities with applications
- Bounds for symmetric elliptic integrals.
- Inequalities and infinite product formula for Ramanujan generalized modular equation function
- Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters
- Some new inequalities of Hermite-Hadamard type for \(s\)-convex functions with applications
- On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
- Refinements of transformation inequalities for zero-balanced hypergeometric functions
- On certain inequalities for means
- On certain means of two arguments and their extensions
- On certain inequalities for means. II
- Optimal Lehmer mean bounds for the Toader mean
- Sharp bounds for the arithmetic-geometric mean
- Sharp bounds for generalized elliptic integrals of the first kind
- Inequalities and bounds for elliptic integrals
- On rational bounds for the gamma function
- An optimal power mean inequality for the complete elliptic integrals
- Some monotonicity properties of generalized elliptic integrals with applications
- Optimal inequalities between Neuman-Sándor, centroidal and harmonic means
- The optimal convex combination bounds of arithmetic and harmonic means in terms of power mean
- Inequalities for the ratio of complete elliptic integrals
- Schur convexity and Hadamard's inequality
- Some properties for a class of symmetric functions and applications
- Hölder mean inequalities for the complete elliptic integrals
- Inequalities for weighted sums of powers and their applications
- The Schur multiplicative and harmonic convexities of the complete symmetric function
- Asymptotic Expansion of the First Elliptic Integral
- Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
- Generalizations of the Logarithmic Mean
- Sharp inequalities for the complete elliptic integral of the first kind
- Eine Methode, die Positivität einer Funktion zu prüfen
- A monotonicity property involving the generalized elliptic integral of the first kind
- Sharp Gautschi inequality for parameter 0<p<1 with applications
- Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind
- On approximating the error function
- Landen inequalities for a class of hypergeometric functions with applications
- Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function
- Sharp Estimates for Complete Elliptic Integrals
- Duplication inequalities for the ratios of hypergeometric functions
- An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse
- Optimal inequalities for the convex combination of error function
- Sharp bounds for Toader mean in terms of contraharmonic mean with applications
- On certain inequalities for means. III
- An arithmetic-geometric mean inequality
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