A Note on Frobenius–Tangent–Fibonacci Polynomials

Resumo

In this study, we develop a new family of two-variable Frobenius–Tangent–Fibonacci polynomials
and their corresponding numerical sequences within the framework of the Golden
F–Calculus. By employing generating functions, we establish several essential algebraic and
analytic properties, including recurrence relations, summation formulas, symmetry identities,
and F–derivative representations. Moreover, we reveal explicit connections between these
polynomials and the Stirling–Fibonacci numbers of the second kind, deriving multiple summation
and convolution-type identities. The framework is further extended through the introduction
of parametric generalizations featuring trigonometric generating mechanisms, which
are explored via F–differential operator methods and functional equations. The results presented
herein broaden the scope of Fibonacci-based special polynomial theory and provide
potential tools for future applications in combinatorics, number theory, approximation theory,
and matrix analysis.