Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind
type: Item
instance of: scholarly article
title: Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind
zbMATH Open document ID: 1492.33003
author: Shen-yang Tan
author: Ti-Ren Huang
author: Yu-Ming Chu
published in: Mathematica Slovaca
publication date: 2021-12-03T00:00:00Z
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 7438370
zbMATH Keywords: Gaussian hypergeometric function
zbMATH Keywords: functional inequality
zbMATH Keywords: generalized elliptic integral
MaRDI profile type: Publication
full work available at URL: ms-2021-0012
OpenAlex ID: W3175012338
cites work: Q5558293
cites work: A note on a function involving complete elliptic integrals: monotonicity, convexity, inequalities
cites work: Inequalities for Zero-Balanced Hypergeometric Functions
cites work: Q3245415
cites work: Hölder mean inequalities for the complete elliptic integrals
cites work: Inequalities between arithmetic-geometric, Gini, and Toader means
cites work: Optimal Lehmer mean bounds for the Toader mean
cites work: Concavity of the complete elliptic integrals of the second kind with respect to Hölder means
cites work: Optimal combinations bounds of root-square and arithmetic means for Toader mean
cites work: Bounds for complete elliptic integrals of the second kind with applications
cites work: Improvements of the bounds for Ramanujan constant function
cites work: Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function
cites work: Bounds for the perimeter of an ellipse in terms of power means
cites work: Optimal bounds for the generalized Euler-Mascheroni constant
cites work: Monotonicity properties and inequalities for the generalized elliptic integral of the first kind
cites work: Monotonicity properties and bounds for the complete \(p\)-elliptic integrals
cites work: Macroscopic Schoen conjecture for manifolds with nonzero simplicial volume
cites work: A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers
cites work: Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters
cites work: Approximation for the complete elliptic integral of the first kind
cites work: Sharp Landen transformation inequalities for hypergeometric functions, with applications
cites work: Landen inequalities for hypergeometric functions
cites work: Sharp rational bounds for the gamma function
cites work: Inequalities for the generalized weighted mean values of \(g\)-convex functions with applications
cites work: Refinements of transformation inequalities for zero-balanced hypergeometric functions
cites work: Landen inequalities for a class of hypergeometric functions with applications
cites work: Precise bounds for the weighted Hölder mean of the complete \(p\)-elliptic integrals
cites work: Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
cites work: Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind
cites work: Asymptotic expansion and bounds for complete elliptic integrals
cites work: Bounds for the perimeter of an ellipse
cites work: An optimal power mean inequality for the complete elliptic integrals
cites work: Asymptotical formulas for Gaussian and generalized hypergeometric functions
cites work: Monotonicity and inequalities involving zero-balanced hypergeometric function
cites work: Sharp power mean inequalities for the generalized elliptic integral of the first kind
cites work: Inequalities and infinite product formula for Ramanujan generalized modular equation function
cites work: On approximating the Toader mean by other bivariate means
cites work: Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function
cites work: Generalized Hersch-Pfluger distortion function and complete elliptic integrals
cites work: A power mean inequality for the Grötzsch ring function
cites work: A power mean inequality involving the complete elliptic integrals
cites work: Monotonicity, convexity and inequalities involving the generalized elliptic integrals
cites work: A monotonicity property involving the generalized elliptic integral of the first kind
cites work: Monotonicity criterion for the quotient of power series with applications
cites work: Sharp bounds for psi function
cites work: Necessary and sufficient conditions for functions involving the psi function to be completely monotonic
cites work: High accuracy asymptotic bounds for the complete elliptic integral of the second kind
cites work: Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
cites work: Monotonicity rule for the quotient of two functions and its application
cites work: On rational bounds for the gamma function
cites work: On approximating the error function
cites work: On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
cites work: Notes on the complete elliptic integral of the first kind
cites work: Sharp inequalities for the generalized elliptic integrals of the first kind
cites work: Sharp Gautschi inequality for parameter 0<p<1 with applications
cites work: Logarithmically complete monotonicity properties relating to the gamma function
cites work: On some refinements for inequalities involving zero-balanced hypergeometric function
cites work: Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means
cites work: A sharp double inequality involving generalized complete elliptic integral of the first kind
cites work: Quadratic transformation inequalities for Gaussian hypergeometric function
cites work: Monotonicity properties of a function involving the psi function with applications
cites work: On approximating the quasi-arithmetic mean

Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind (DOI)
DOI: 10.1515/MS-2021-0012