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

ŞİMŞEK Y.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.14, no.3, pp.627-640, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.2298/aadm190220042s
  • Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.627-640
  • Keywords: Special sequences and polynomials, Generating functions, Fibonacci numbers, Bernoulli numbers, Euler numbers, Stirling numbers, Functional equations Binomial coefficients, Combinatorial identities, APOSTOL-TYPE NUMBERS
  • Akdeniz University Affiliated: Yes

Abstract

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.