A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL

Authors : A D Godase, M B Dhakne

Pages : 1-19

View : 12 | Download : 8

Publication Date : 2017-11-01

Article Type : Research Paper

Abstract :The Fibonacci polynomial Fninsert ignore into journalissuearticles values(x); defined recurrently by Fn+1insert ignore into journalissuearticles values(x); = xFninsert ignore into journalissuearticles values(x);+Fn−1insert ignore into journalissuearticles values(x);, with F0insert ignore into journalissuearticles values(x); = 0, F1insert ignore into journalissuearticles values(0); = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1insert ignore into journalissuearticles values(x); and Lbn+1insert ignore into journalissuearticles values(x); are introduced and defined by Fbn+1insert ignore into journalissuearticles values(x); = xFbninsert ignore into journalissuearticles values(x);+Fbn−1insert ignore into journalissuearticles values(x); with Fb0insert ignore into journalissuearticles values(x); = 0, Fb1insert ignore into journalissuearticles values(x); = x 2+4, for n ≥ 1 and Lbn+1insert ignore into journalissuearticles values(x); = xLbninsert ignore into journalissuearticles values(x);+Lbn−1insert ignore into journalissuearticles values(x); with Lb0insert ignore into journalissuearticles values(x); = 2x 2 + 8, Lb1insert ignore into journalissuearticles values(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