Optimal power-type Heronian and Lehmer means inequalities for the complete elliptic integrals

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2024-08-23 DOI:10.1080/10652469.2024.2392281

Chen Hai-sheng, Zhu Ye-cheng

引用次数: 0

Abstract

In this paper, we prove that the inequalities Hp(K(r),E(r))<π2,Lq(K(r),E(r))<π2 hold for all r∈(0,1) if and only if p≤−log⁡3/log⁡(π/2) and q<−1, where Hp(a,b) and Lq(a,b) are respectively the p-th...

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完全椭圆积分的最优幂型赫伦和雷默均值不等式

本文证明，当且仅当 p≤-log3/log(π/2) 和 q<-1 时，对于所有 r∈(0,1)，不等式 Hp(K(r),E(r))<π2,Lq(K(r),E(r))<π2 成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.