Bounds for novel extended beta and hypergeometric functions and related results

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-05 DOI:10.1186/s13660-024-03148-8

Rakesh K. Parmar, Tibor K. Pogány

引用次数: 0

Abstract

We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.

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新型扩展贝塔函数和超几何函数的边界及相关结果

我们引入了欧拉贝塔函数积分形式的一个新的统一扩展，其积分中包含一个麦克唐纳函数，并为其建立了函数上界。我们利用这一定义扩展了高斯和库默尔汇合超几何函数，并为其提供了边界不等式。此外，我们利用贝塔函数的扩展定义了一种新的概率分布，并为其建立了原始矩和矩量不等式，作为副产品，我们还为最初定义的扩展贝塔函数建立了图兰不等式。

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

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.