由若干特殊数的生成函数导出奈万林纳特征函数的计算。

IF 1.6 3区数学 Q1 Mathematics Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-07 DOI:10.1186/s13660-018-1722-y

Serkan Araci, Mehmet Acikgoz

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引用次数: 3

摘要

本文首先求出伯努利数及其相关欧拉数的生成函数的若干极点，分别记为n(a,B)和n(a,E)。其次，我们推导了伯努利数和相关欧拉数的生成函数的正对数的平均值，分别表示为m(2π，B)和m(π，E)。从这些性质中，我们得到了本文所述的奈万林纳特征函数。最后，作为一个应用，证明了伯努利数的生成函数是一个正态函数。

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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Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers.

In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by $n (a, B)$ and $n (a, E)$ , respectively. Secondly, we derive the mean value of a positive logarithm of generating functions of Bernoulli numbers and associated Euler numbers shown as $m (2 π, B)$ and $m (π, E)$ , respectively. From these properties, we find Nevanlinna characteristic functions which we stated in the paper. Finally, as an application, we show that the generating function of Bernoulli numbers is a normal function.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

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.