On generalized Fibonacci and Lucas hybrid polynomials

Authors

N. ROSA AIT-AMRANE
HACENE BELBACHIR
ELİF TAN

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.

DOI

10.55730/1300-0098.3254

Keywords

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

First Page

2069

Last Page

2077

Recommended Citation

AIT-AMRANE, N. R, BELBACHIR, H, & TAN, E (2022). On generalized Fibonacci and Lucas hybrid polynomials. Turkish Journal of Mathematics 46 (6): 2069-2077. https://doi.org/10.55730/1300-0098.3254