Monotonicity properties and inequalities for the generalized elliptic integral of the first kind

被引：20

作者：

Huang, Ti-Ren ^{[1
]}

Qiu, Song-Liang ^{[1
]}

Ma, Xiao-Yan ^{[1
]}

机构：

[1] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 469卷 / 01期

关键词：

Generalized elliptic integrals of the first kind; Complete elliptic integrals of the first kind; Gaussian hypergeometric function; Ramanujan constant (or R-function); Monotonicity; Concavity; Sharp inequalities; BALANCED HYPERGEOMETRIC-FUNCTIONS; FUNCTIONAL INEQUALITIES; TRANSFORMATION INEQUALITIES; RATIOS;

D O I：

10.1016/j.jmaa.2018.08.061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The authors obtain some monotonicity and concavity properties, and asymptotically sharp bounds for the generalized elliptic integral k(a)(gamma) of the first kind and its special case k(gamma), the complete elliptic integral of the first kind, by studying the monotonicity and concavity properties of certain combinations defined in terms of the Gaussian hypergeometric function F (a, 1 - a; 1; x) and elementary functions, thus improving some well-known results. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：95 / 116

页数：22

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