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.

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

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