A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL

Year 2017, Issue: 19, 1 - 19, 01.11.2017

A. D. Godase M. B. Dhakne

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