On the Derivatives of Bivariate Fibonacci Polynomials

TL;DR

This paper explores new algebraic properties of bivariate Fibonacci polynomials, deriving their partial derivatives and establishing a recurrence relation for their derivatives, advancing theoretical understanding of these polynomials.

Contribution

It introduces novel algebraic properties and a recurrence relation for derivatives of bivariate Fibonacci polynomials, expanding their mathematical framework.

Findings

Partial derivatives expressed as convolutions of bivariate Fibonacci polynomials

New recurrence relation for the r-th partial derivatives

Enhanced theoretical understanding of bivariate Fibonacci polynomials

Abstract

In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a new recurrence relation for the r-th partial derivative sequence of bivariate Fibonacci polynomials.