Bernoulli F-polynomials and Fibo-Bernoulli matrices


Kus S., Tuğlu N. , Kim T.

ADVANCES IN DIFFERENCE EQUATIONS, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1186/s13662-019-2084-6
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS

Özet

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.