一类广义椭圆积分的单调性定理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.2298/aadm201005031b

Qi Bao, Xue-Jing Ren, Miao-Kun Wang

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引用次数: 1

摘要

为了一个?(0,1/2)和r ?(0,1)，设Ka(r) (K (r))表示第一类广义椭圆积分(分别为完全椭圆积分)。本文主要给出了函数a ?(K (r) - ka (r)) = (1-2a) ? (? ?R)在(0,1/2)上是单调的对于每个固定的R ?(0, 1)。由此得出不等式K (r)- (1-2a)?[K(r)- ?/2] ?Ka (r) ?K (r) - (1-2a) ?[K (r) - ?/2]适用于所有a ?(0,1/2)和r ?(0,1)用最好的常数?= ?/2和?= 2。

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A monotonicity theorem for the generalized elliptic integral of the first kind

For a ? (0,1/2] and r ? (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete elliptic integral, respectively) of the first kind. In this article, we mainly present a sufficient and necessary condition under which the function a ? [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed r ? (0,1). The obtained result leads to the conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] ? Ka(r) ? K (r)-(1-2a)? [K(r)-?/2] holds for all a ? (0,1/2] and r ? (0,1) with the best possible constants ? = ?/2 and ? = 2.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.