Bivariate Vieta-Fibonacci and Bivariate Vieta-Lucas Polynomials

Abstract

In this paper, we consider the bivariate Vieta-Fibonacci and bivariate Vieta-Lucas polynomials which are generalized of Vieta-Fibonacci, Vieta-Lucas, Vieta-Pell, Vieta-Pell-Lucas polynomials. Also, we give the some properties. Afterwards, we obtain the some identities for the bivariate Vieta-Fibonacci and bivariate Vieta-Lucas polynomials by using the known properties of bivariate Vieta-Fibonacci and bivariate Vieta-Lucas polynomials.

Vieta–Fibonacci-like polynomials and some identities

“…The first few terms of the Vieta-Fibonacci polynomials sequence are 0, 1, , 2 − 1, 3 − 2 , 4 − 3 2 + 1 and the first few terms of the Vieta-Lucas polynomials sequence are 2, , 2 − 2, 3 are the roots the characteristic equation 2 − +1 = 0. We also note that ( )+ ( ) = , ( ) ( ) = 1, and ( ) − ( ) = √ 2 − 4.…”

Symmetric and generating functions for some generalized polynomials

“…Definition 1.1. [6] For any integer n ≥ 0, the trivariate Fibonacci polynomials, denoted by {H n (x, y,t)} n≥0 is defined recursively by…”

Some Properties of Bivariate Fibonacci and Lucas Quaternion Polynomials

“…Some authors considered special sequence polynomials for example generalized Fibonacci and Lucas polynomials in [7] and also bivariate Fibonacci and Lucas like polynomials in [6].…”