A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL

Abstract

The Fibonacci polynomial Fn(x) defined recurrently by Fn+1(x) = xFn(x)+Fn−1(x), with F0(x) = 0, F1(0) = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1(x) and Lbn+1(x) are introduced and defined by Fbn+1(x) = xFbn(x)+Fbn−1(x) with Fb0(x) = 0, Fb1(x) = x 2+4, for n ≥ 1 and Lbn+1(x) = xLbn(x)+Lbn−1(x) with Lb0(x) = 2x 2 + 8, Lb1(x) = x 3 + 4x, for n ≥ 1. Also some basic properties of these polynomials are obtained by matrix methods.

Keywords

• −Fibonacci Sequence, Fibonacci Polynomial, Generalised Fibonacci Polynomial