与彼得斯数和多项式相关的一组新的组合数和多项式

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2020-01-01 DOI:10.2298/aadm190220042s

Y. Simsek

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引用次数: 8

摘要

本文的目的是定义与彼得斯多项式相关的新的组合数和多项式族。这些族也是[11]中特殊数和多项式的修正。给出了这些多项式和数的一些基本性质。此外，利用二项式系数计算斐波那契数的组合恒等式(由Lucas于1876年证明)，用不同的方法证明了它。因此，用同样的方法，我们给出了一个新的Fibonacci数和Lucas数的递归式。最后，给出了这些组合数与多项式及其生成函数之间的关系，以及其他已知的特殊多项式与数之间的关系。

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A new family of combinatorial numbers and polynomials associated with peters numbers and polynomials

The aim of this paper is to define new families of combinatorial numbers and polynomials associated with Peters polynomials. These families are also a modification of the special numbers and polynomials in [11]. Some fundamental properties of these polynomials and numbers are given. Moreover, a combinatorial identity, which calculates the Fibonacci numbers with the aid of binomial coefficients and which was proved by Lucas in 1876, is proved by different method with the help of these combinatorial numbers. Consequently, by using the same method, we give a new recurrence formula for the Fibonacci numbers and Lucas numbers. Finally, relations between these combinatorial numbers and polynomials with their generating functions and other well-known special polynomials and numbers are given.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).