论文标题
对某些类型的Apostol-type多项式的计算公式和与这些多项式相关的某些属性
Implementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials
论文作者
论文摘要
本文的主要目的是为某些类型的使徒型数和多项式提供各种身份和计算公式。本文的结果不仅包含$λ$ -Apostol-Daehee数字和多项式，还包含Simsek的数字和多项式，第一类的Stirling数字，Daehee数字和Chu-Vandermonde身份。此外，我们得出了$λ$ -Apostol-Daehee多项式的无限级数表示。通过使用包含Cauchy数字生成函数的功能方程，以及$λ$ -Apostol-Daehee数和多项式的生成函数的Riemann积分，我们还为这些数字和多项式提供了一些身份和公式。此外，我们通过Wolfram语言为Mathematica中的$λ$ -Apostol-Daehee多项式提供了计算公式。通过这种实现，我们还提供了这些多项式的一些图，以研究其行为的一些随机选择的参数特殊情况。最后，我们对我们的结果进行了一些评论和观察，总结了本文。
The main purpose of this paper is to present various identities and computation formulas for certain classes of Apostol-type numbers and polynomials. The results of this paper contain not only the $λ$-Apostol-Daehee numbers and polynomials, but also Simsek numbers and polynomials, the Stirling numbers of the first kind, the Daehee numbers, and the Chu-Vandermonde identity. Furthermore, we derive an infinite series representation for the $λ$-Apostol-Daehee polynomials. By using functional equations containing the generating functions for the Cauchy numbers and the Riemann integrals of the generating functions for the $λ$-Apostol-Daehee numbers and polynomials, we also derive some identities and formulas for these numbers and polynomials. Moreover, we give implementation of a computation formula for the $λ$-Apostol-Daehee polynomials in Mathematica by Wolfram language. By this implementation, we also present some plots of these polynomials in order to investigate their behaviour some randomly selected special cases of its parameters. Finally, we conclude the paper with some comments and observations on our results.
