第一类修正贝塞尔函数中Toader-Qi均值的新锐界

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.7153/jmi-2022-16-44

Cen Li, Zhi-Ming Liu, Shenzhou Zheng

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引用次数: 1

摘要

设A(A,b)、G(A,b)、L (A,b)和TQ(A,b)分别为A,b和b的算术均值、几何均值、对数均值和Toader-Qi均值。设Iv (x)是第一类v阶的修正贝塞尔函数。我们证明了二重不等式√sinh t t Uq (t) < I0 (t) <√sinh t t Up (t)对t >成立，或者等价地，√L (a,b)Uq (a,b) < TQ(a,b) <√L (a,b)Up (a,b)，当且仅当p 11/15和0 < q 2/π，其中Up (t) = pcosh t−4 (p−2 3)，当a = b时，对a,b >成立。

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On new sharp bounds for the Toader-Qi mean involved in the modified Bessel functions of the first kind

Let A(a,b) , G(a,b) , L (a,b) and TQ(a,b) be the arithmetic, geometric, logarithmic and Toader-Qi means of a,b > 0 with a = b , respectively. Let Iv (x) be the modified Bessel functions of the first kind of order v . We prove the double inequality √ sinh t t Uq (t) < I0 (t) < √ sinh t t Up (t) holds for t > 0 , or equivalently, √ L (a,b)Uq (a,b) < TQ(a,b) < √ L (a,b)Up (a,b), holds for a,b > 0 with a = b , if and only if p 11/15 and 0 < q 2/π , where Up (t) = pcosh t−4 ( p− 2 3 )

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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.