新型扩展贝塔函数和超几何函数的边界及相关结果

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-06-05 DOI:10.1186/s13660-024-03148-8

Rakesh K. Parmar, Tibor K. Pogány

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引用次数: 0

摘要

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。

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Bounds for novel extended beta and hypergeometric functions and related results

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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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.