On generalized Fibonacci and Lucas hybrid polynomials

Authors

N. ROSA AIT-AMRANE
HACENE BELBACHIR
ELİF TAN

DOI

10.55730/1300-0098.3254

Abstract

In this paper, we introduce a new generalization of Fibonacci and Lucas hybrid polynomials. We investigate some basic properties of these polynomials such as recurrence relations, the generating functions, the Binet formulas, summation formulas, and a matrix representation. We derive generalized Cassini's identity and generalized Honsberger formula for generalized Fibonacci hybrid polynomials by using their matrix representation.

Keywords

$r$-Fibonacci polynomial, $r$-Lucas polynomial, hybrid number

First Page

2069

Last Page

2077

Recommended Citation

AIT-AMRANE, N. ROSA; BELBACHIR, HACENE; and TAN, ELİF (2022) "On generalized Fibonacci and Lucas hybrid polynomials," Turkish Journal of Mathematics: Vol. 46: No. 6, Article 2. https://doi.org/10.55730/1300-0098.3254
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/2