New Generalized Biparametric Fubini-type Polynomials of Level-$m$

This paper introduces two new biparametric families of generalized Fubini-type polynomials of level-m A [m−1,α] n,c (x, y, a) and A [m−1,α] n,s (x, y, a). We give some algebraic and differential properties, as well as relationships between these classes of polynomials with other polynomials and numbers. In addition, we introduce the new generalized biparametric Fubini-type polynomials matrices D [m−1,α] c (x, y; a) and D [m−1,α] s (x, y; a). As a result, we derive the product formula for D [m−1,α] c (x, y; a) and D [m−1,α] s (x, y; a) and provide some factorizations of biparametric Fubini-type polynomials matrix D [m−1,α] c (x, y; a) and D [m−1,α] s (x, y; a), which involve the generalized Pascal matrix.