On Bivariate Fibonacci-Fubini Polynomials

Abstract

Recently, Fibonacci extensions of several special polynomials, such as Fibonacci-Hermite, Fibonacci-Euler, Fibonacci-Genocchi, Fibonacci-Bernoulli, and Fibonacci-Bernstein polynomials have been considered and diverse of their properties and relations have been thoroughly analyzed using the content of Golden calculus. In this paper, we first define the generating function of the bivariate Fibonacci-Fubini polynomials and derive some valuable relations and properties. These involve summation formulas, addition formulas, golden derivative property, and golden integral representation for the bivariate Fibonacci-Fubini polynomials. We also provide implicit summation formulas and a symmetric identity for these polynomials. Moreover, we investigate multifarious correlations and formulas for the bivariate Fibonacci-Fubini polynomials associated with the Fibonacci-Euler polynomials, the Fibonacci-Bernoulli polynomials, and the Fibonacci-Stirling polynomials of the second kind. Lastly, we provide a Fibonacci differential operator formula for the bivariate Fibonacci-Fubini polynomials.