On the Generalized Fibonacci and Lucas Matrix Hybrinomials

Abstract

Hybrid numbers, which as a generalization of complex, dual and hyperbolic numbers, are widely used in a variety of fields. Through a novel approach, this study aims to obtain the generalized Fibonacci matrix hybrinomials by virtue of the bi--periodic Fibonacci matrix polynomials. Moreover, we give the definition of the bi--periodic Lucas matrix polynomials unlocking their specific properties. Then, we obtain the generalized Lucas matrix hybrinomials via bi--periodic Lucas polynomials and leveraging these findings. Ultimately, we give the generating function, Binet's formula and a few summation formulas for the generalized Fibonacci and Lucas matrix hybrinomials.