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.
$r$-Fibonacci polynomial, $r$-Lucas polynomial, hybrid number
AIT-AMRANE, N. ROSA; BELBACHIR, HACENE; and TAN, ELİF
"On generalized Fibonacci and Lucas hybrid polynomials,"
Turkish Journal of Mathematics: Vol. 46:
6, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/2