On the Convexity and Concavity of Generalized Complete Elliptic Integral of the First Kind

被引：6
|
作者：
Chen, Ya-jun [1 ]
Zhao, Tie-hong [1 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2022年 / 77卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Complete elliptic integrals; generalized complete elliptic integrals; convexity; concavity; FUNCTIONAL INEQUALITIES; GAMMA FUNCTION; MONOTONICITY;
D O I：
10.1007/s00025-022-01755-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the convexity (concavity) of the function x bar right arrow K-a(root x) - log(1 + c/root 1-x) on (0, 1) for a is an element of (0,1/2] and c is an element of (0,infinity), where K-a(r) is the generalized complete elliptic integral of the first kind. This work is an extension of Yang and Tian (Appl Anal Discrete Math 13:240-260, 2019), and also gives a refinement of inequality (Yang and Tian 2019, 0.27) as an application.
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页数：20
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