A study of discrete U-Frobenius–Euler type polynomials and generalized discrete orthogonal U-Frobenius–Euler type polynomials

In this paper, we introduce two new families of discrete polynomials: The UFrobenius–Euler type discrete polynomials and the generalized discrete orthogonal U-Frobenius–Euler type polynomials. We provide explicit expressions, recurrence relations, algebraic and differential properties, and significant identities for both families. Furthermore, we define an orthogonality relation for the generalized discrete U-Frobenius–Euler type polynomials, which plays a key role in understanding other properties of this family of polynomials. This exploration strengthens the theoretical framework around these polynomial families and also lays the foundation for future research in discrete mathematics.