q-Extensions of Some Results Involving the Luo-Srivastava Generalizations of the Apostol-Bernoulli and Apostol-Euler Polynomials
q-Extensions of Some Results Involving the Luo-Srivastava Generalizations of the Apostol-Bernoulli and Apostol-Euler Polynomials
复制标题
DOI：
10.2298/fil1402329l
复制
发表时间：
2014-09
期刊：
影响因子：
0.8
通讯作者：
Qiu-Ming Luo
中科院分区：
文献类型：
--
作者：
Qiu-Ming Luo
Carlitz首先定义了$q$-Bernoulli和$q$-Euler多项式[\texit {杜克数学J.}，（1948），987- 1000]。最近，M。Cenkci和M.可以[\textit{高级螺柱。数学}，\textbf{12}（2006），213--223]，J. Choi，P. J.安德森和H. M. Srivastava [ \textit{Appl. Math. Comput.}，{\bf199}（2008），723--737]进一步定义了$q$-Apostol-Bernoulli和$q$-Apostol-Euler多项式。本文给出了$q$-Apostol-Bernoulli和$q$-Apostol-Euler多项式的生成函数和基本性质，得到了$q$-Apostol-Bernoulli和$q$-Apostol-Euler多项式之间的一些关系，它们是某些已知结果的$q$-推广。还考虑了第二类q$-斯特林数级数中的一些公式。
Carlitz firstly defined the $q$-Bernoulli and $q$-Euler polynomials [\textit{Duke Math. J.}, \textbf{15} (1948), 987--1000]. Recently, M. Cenkci and M. Can [\textit{Adv. Stud. Contemp. Math.}, \textbf{12} (2006), 213--223], J. Choi, P. J. Anderson and H. M. Srivastava [ \textit{Appl. Math. Comput.}, {\bf199} (2008), 723--737] further defined the $q$-Apostol-Bernoulli and $q$-Apostol-Euler polynomials. In this paper, we show the generating functions and basic properties of the $q$-Apostol-Bernoulli and $q$-Apostol-Euler polynomials, and obtain some relationships between the $q$-Apostol-Bernoulli and $q$-Apostol-Euler polynomials which are the corresponding $q$-extensions of some known results. Some formulas in series of $q$-Stirling numbers of the second kind are also considered.