Bivariate Gaussian Fibonacci and Lucas Polynomials

Abstract

In this study, we define and investigate the Bivariate Gaussian Fibonacci and Bivariate Gaussian Lucas Polynomials. We derive generating functions, Binet formulas, explicit formulas, and partial derivatives of these polynomials. By defining these bivariate polynomials for special cases, we obtain:\(F_n(x, 1)\) as the Gaussian Fibonacci polynomials,\(L_n(x, 1)\) is the Gaussian Lucas polynomials,\( {F}_{n}(1, 1)\) as the Gaussian Fibonacci numbers, and \( {L}_{n}(1, 1)\) as the Gaussian Lucas numbers, as defined in \([19]\).