Topics in Special Functions III
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Publication:3193150
DOI10.1007/978-1-4939-0258-3_11zbMath1323.33001arXiv1209.1696OpenAlexW2065775613MaRDI QIDQ3193150
Xiao-Hui Zhang, Matti Vuorinen, Glenn D. Anderson
Publication date: 15 October 2015
Published in: Analytic Number Theory, Approximation Theory, and Special Functions (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1209.1696
Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Research exposition (monographs, survey articles) pertaining to special functions (33-02) Inequalities for trigonometric functions and polynomials (26D05)
Related Items
About some exponential inequalities related to the sinc function ⋮ Sharp bounds for gamma function in terms of \(x^{x - 1}\) ⋮ The inverse hyperbolic tangent function and Jacobian sine function ⋮ Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities ⋮ Refined estimates and generalizations of inequalities related to the arctangent function and Shafer's inequality ⋮ Inequalities for the generalized trigonometric and hyperbolic functions ⋮ ON THE GENERALIZED CONVEXITY AND CONCAVITY ⋮ The visual angle metric and quasiregular maps ⋮ Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach ⋮ Generalizations and improvements of approximations of some analytic functions: a survey ⋮ Some inequalities for the generalized sine and the generalized hyperbolic sine ⋮ A short proof of Burnside's formula for the gamma function ⋮ Monotonicity criterion for the quotient of power series with applications
Cites Work
- Some bounds for the complete elliptic integrals of the first and second kinds
- A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in $n$-space
- On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
- A Recursive Scheme for Improving the Original Rate of Convergence to the Euler—Mascheroni Constant
- A power mean inequality for the Grötzsch ring function
- A monotonicity property of Euler's gamma function
- Power series inequalities via Buzano's result and applications
- A Quicker Convergence to Euler's Constant
- On generalized complete elliptic integrals and modular functions
- On the asymptotic expansion of the logarithm of Barnes triple gamma function
- Hölder mean inequalities for the generalized Grötzsch ring and Hersch-Pfluger distortion functions
- A general refinement of Jordan's inequality and a refinement of L. Yang's inequality
- Turán type inequalities for hypergeometric functions
- Monotonicity Rules in Calculus
- L'Hospital Rules for Monotonicity and the Wilker-Anglesio Inequality
- Very accurate estimates of the polygamma functions
- Extensions of the generalized Wilker inequality to Bessel functions
- On a quadratic estimate of Shafer
- Remarks on generalized elliptic integrals
- An Optimal Two Parameter Bounds for the Identric Mean
- SHARP INEQUALITIES FOR FACTORIAL n
- Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
- Generalizations of the Logarithmic Mean
- Landen inequalities for hypergeometric functions
- A monotoneity property of the gamma function
- Asymptotic expansions and inequalities for hypergeometric function
- Completely monotonic functions
- Sharp inequalities for the digamma and polygamma functions
- On some properties of the Gamma function
- Some properties of the gamma and psi functions, with applications
- Inequalities for the gamma function
- New sharp bounds for identric mean in terms of logarithmic mean and arithmetic mean
- A note on a certain bivariate mean
- Duplication inequalities for the ratios of hypergeometric functions
- Bounds for the ratios of differences of power means in two arguments
- Bernoulli inequality and hypergeometric functions
- Inequalities for eigenfunctions of the $p$-Laplacian
- A weighted and exponential generalization of Wilker's inequality and its applications
- Topics in special functions. II
- SOME INEQUALITIES FOR THE GENERALIZED GRÖTZSCH FUNCTION
- A general form of Jordan's inequalities and its applications
- A Hypergeometric Mean Value
- Some Inequalities for Hypergeometric Functions
- A Property of the Hypergeometric Mean Value
- Inequalities for a Symmetric Elliptic Integral
- Analytic Inequalities
- On Quadratic Approximation
- On some inequalities for the gamma and psi functions
- Sharpness and generalization of Jordan's inequality and its application
- Inequalities for the generalized trigonometric and hyperbolic functions
- On certain inequalities for means. III
- On hypergeometric functions and generalizations of Legendre's relation
- A completely monotone function related to the gamma function
- On the asymptotic representation of the Euler gamma function by Ramanujan
- Optimal combinations bounds of root-square and arithmetic means for Toader mean
- Monotonicity and logarithmic convexity relating to the volume of the unit ball
- On exterior moduli of quadrilaterals and special functions
- On quotients and differences of hypergeometric functions
- Sharp Cusa and Becker-Stark inequalities
- Refinements of Jordan's inequality
- New upper bounds of \(n!\)
- Sharpness of Wilker and Huygens type inequalities
- Landen inequalities for zero-balanced hypergeometric functions
- A note on Jordan type inequalities for hyperbolic functions
- Absolutely (completely) monotonic functions and Jordan-type inequalities
- A completely monotonic function used in an inequality of Alzer
- Bounds for the perimeter of an ellipse
- Bounds for complete elliptic integrals of the second kind with applications
- On Shafer and Carlson inequalities
- Ramanujan's estimate for the gamma function via monotonicity arguments
- Extension of Redheffer type inequalities to modified Bessel functions
- Sharp power mean bounds for the Gaussian hypergeometric function
- Bounds for complete elliptic integrals of the first kind
- On Jordan type inequalities for hyperbolic functions
- Inequalities for the harmonic numbers
- Generalized Jacobian elliptic functions and their application to bifurcation problems associated with \(p\)-Laplacian
- On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function
- New sharp bounds for the Bernoulli numbers and refinement of Becker-Stark inequalities
- Inequalities for the generalized elliptic integrals with respect to Hölder means
- Inequalities for differences of power means in two variables
- An extended Jordan's inequality in exponential type
- Hypergeometric analogues of the arithmetic-geometric mean iteration
- Monotonicity theorems and inequalities for the complete elliptic integrals
- A new weighted metric: the relative metric. II
- Inequalities and bounds for generalized complete elliptic integrals
- Inequalities for the Euler-Mascheroni constant
- On an absolute constant in the theory of quasi-conformal mappings
- Functional inequalities involving special functions. II
- On some properties of digamma and polygamma functions
- Inequalities for the generalized elliptic integrals and modular functions
- Turán type inequalities for generalized complete elliptic integrals
- Functional inequalities involving Bessel and modified Bessel functions of the first kind
- A general refinement of Jordan-type inequality
- Jordan-type inequalities for differentiable functions and their applications
- Sharpening the Becker-Stark inequalities
- Generalized Bessel functions of the first kind
- A source of inequalities for circular functions
- Some new inequalities of the Huygens type
- Jordan type inequalities involving the Bessel and modified Bessel functions
- On new sequences converging towards the Euler-Mascheroni constant
- Six new Redheffer-type inequalities for circular and hyperbolic functions
- New inequalities of Shafer-Fink type for arc hyperbolic sine
- Convexity with respect to Hölder mean involving zero-balanced hypergeometric functions
- Sharpening Redheffer-type inequalities for circular functions
- Some new Wilker-type inequalities for circular and hyperbolic functions
- Refinements, generalizations, and applications of Jordan's inequality and related problems
- Generalizations of Shafer-Fink-type inequalities for the arc sine function
- Inequalities and monotonicity of ratios for generalized hypergeometric function
- New approximations of the gamma function in terms of the digamma function
- Special functions of quasiconformal theory
- Some remarkable sine and cosine functions
- Inequalities for quasiconformal mappings in space
- Functional inequalities for the quotients of hypergeometric functions
- Some mean values related to the arithmetic-geometric mean
- Inequalities for means in two variables
- Pick functions related to the gamma function.
- On generalized trigonometric functions with two parameters
- Homogeneous mean values: weights and asymptotics
- Inequalities for the volume of the unit ball in \(\mathbb{R}^n\)
- Elliott's identity and hypergeometric functions
- A new weighted metric: the relative metric. I
- Optimal Lehmer mean bounds for the Toader mean
- Some inequalities for the generalized linear distortion function
- Asymptotical bounds for complete elliptic integrals of the second kind
- Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
- Log-convexity and log-concavity for series in gamma ratios and applications
- A general form of Jordan-type double inequality for the generalized and normalized Bessel functions
- Generalized elliptic integrals
- Generalized convexity and inequalities involving special functions
- Inequalities for the volume of the unit ball in \(\mathbb{R}^n\). II
- On some properties of the gamma function
- Concavity with respect to Hölder means involving the generalized Grötzsch function
- Computing the \(\sin_p\) function via the inverse power method
- Monotonicity properties of the gamma function
- On the strengthened Jordan's inequality
- Generalized elliptic integrals and the Legendre \(\mathcal M\)-function
- A further refinement of a Jordan type inequality and its application
- Functional inequalities involving special functions
- Landen-type inequality for Bessel functions
- The bounds of the solutions to generalized modular equations
- Approximate convexity and concavity of generalized Grötzsch ring function
- Generalization and sharpness of the power means inequality and their applications
- Generalized convexity and inequalities
- On Wilker and Huygens type inequalities
- Two sharp inequalities for trigonometric and hyperbolic functions
- On Kaluza's sign criterion for reciprocal power series
- Hölder concavity and inequalities for Jacobian elliptic functions
- Refinements and sharpness of some new Huygens type inequalities
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