一些广义ζ函数的积分表示及其结果的注释

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI:10.7153/MIA-2021-24-17

K. Mehrez

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引用次数: 1

摘要

。本笔记的主要焦点是建立新的积分表示的Hurwitz-Lerch zeta和多参数的Hurwitz-Lerch zeta函数。特别推导了多对数函数和Fox-Wright函数的新的积分表达式。此外，还建立了zeta分布矩生成函数的闭积分形式表达式。作为应用，我们得到了与Hurwitz-Lerch ζ和多对数函数相关的两类函数的完全单调性。此外，还证明了涉及这两个函数的一些不等式。

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A note on integral representation of some generalized zeta functions and its consequences

. The main focus of the present note is to establish new integral representation for the Hurwitz-Lerch zeta and the multi-parameter Hurwitz-Lerch zeta functions. In particular, new integral expression of the polylogarithm function and the Fox-Wright function are derived. In addition, closed integral form expression of the moment generating function of a zeta distribution is established. As application, we derive the complete monotonicity properties of two classes of function related to the Hurwitz-Lerch zeta and the polylogarithm function. Moreover, some inequalities involving these two functions are proved.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.