Bernoulli F-polynomials and Fibo-Bernoulli matrices


Kus S., Tuğlu N., Kim T.

ADVANCES IN DIFFERENCE EQUATIONS, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2019
  • Doi Number: 10.1186/s13662-019-2084-6
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Bernoulli polynomials, Bernoulli F-polynomials, Euler-Fibonacci numbers, Bernoulli matrices, Generating function
  • Gazi University Affiliated: Yes

Abstract

In this article, we define the Euler-Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler-Fibonacci numbers and the Euler-Fibonacci polynomials. A new exponential generating function is obtained for the Bernoulli F-polynomials. Also, we describe the Fibo-Bernoulli matrix, the Fibo-Euler matrix and the Fibo-Euler polynomial matrix by using the Bernoulli F-polynomials, the Euler-Fibonacci numbers and the Euler-Fibonacci polynomials, respectively. Factorization of the Fibo-Bernoulli matrix is obtained by using the generalized Fibo-Pascal matrix and a special matrix whose entries are the Bernoulli-Fibonacci numbers. The inverse of the Fibo-Bernoulli matrix is also found.