A best possible upper bound for the complete elliptic integral of the first kind

IF 0.4 4区数学 Q4 MATHEMATICS

Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI:10.36045/j.bbms.230228

Zhong-Xuan Mao, Lan-Xiang Yu, Jun-Yi Li, Jing-Feng Tian

引用次数: 0

Abstract

In this paper, we establish a sufficient and necessary condition for a function involving the inverse hyperbolic tangent function as a best possible upper bound for the complete elliptic integral of the first kind. Equivalently, we obtain a lower bound involving the arithmetic mean and logarithmic mean for the Gauss arithmetic-geometric mean. This provides a positive answer to a conjecture proposed by Yang, Song and Chu in 2014.

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第一类完全椭圆积分的最佳可能上界

本文建立了包含逆双曲正切函数的函数作为第一类完全椭圆积分的最佳可能上界的充要条件。同样地，我们得到高斯算术几何平均数的算术平均数和对数平均数的下界。这为Yang、Song和Chu在2014年提出的一个猜想提供了积极的答案。

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

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.