A NEW FAMILY OF COMBINATORIAL NUMBERS AND POLYNOMIALS ASSOCIATED WITH PETERS NUMBERS AND POLYNOMIALS

Applicable Analysis and Discrete Mathematics

article

Yilmaz Simsek¹ 

[1] Department of Mathematics, Faculty of Science University of Akdeniz TR-07058 Antalya

关键词: Special sequences and polynomials;    Generating functions;    Fibonacci numbers;    Bernoulli numbers;    Euler numbers;    Stirling numbers;    Functional equations;    Binomial coefficients;    Combinatorial identities;   

DOI  :  10.2298/AADM190220042S

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

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

【 授权许可】

Unknown