Bivariate Gaussian Fibonacci and Lucas polynomials

Abstract

In this study we define and study the Bivariate Gaussian Fibonacci and Bivariate Gaussian Lucas Polynomials. We give generating function, Binet formula, explicit formula and partial derivation of these polynomials. By defining these bivariate polynomials for special cases Fn(x, 1) is the Gaussian Fibonacci polynomials, Ln(x, 1) is the Gaussian Lucas polynomials, Fn(1, 1) is the Gaussian Fibonacci numbers and L n(1, 1) is the Gaussian Lucas numbers defined in [19].