A note on Gaussian family of the Leonardo polynomials

In this article, we introduce a new member of the Gaussian family of polynomials: the Gauss–Leonardo polynomials. These polynomials extend the classical Leonardo sequence and Fibonacci polynomials into the Gaussian domain. The goal is to develop connection formulae linking the Gauss–Leonardo, Fibonacci, and Lucas polynomials, while deriving fundamental algebraic properties such as Binet-type formula, recurrence relations, norms, and both ordinary and exponential generating functions. We further present series summation identities and explore derivative-based identities. Finally, this study highlights structural connections between the newly defined Gauss–Leonardo polynomials and well-known families, including the Fibonacci, Lucas, and Chebyshev polynomials.