Numerator polynomials of Riordan matrices

Abstract

Riordan matrices are infinite lower triangular matrices corresponding to the certain operators in the space of formal power series. Generalized Euler polynomials gn(x)=(1−x)n+1∑m=0∞pn(m)xm, where pn(m) is the polynomial of degree ≤n, are the numerator polynomials of the generating functions of diagonals of the ordinary Riordan matrices. Generalized Narayana polynomials hn(x)=(1−x)2n+1∑m=0∞(m+1)...(m+n)pn(m)xm are the numerator polynomials of the generating functions of diagonals of the exponential Riordan matrices. In paper, the properties of these two types of numerator polynomials and the constructive relationships between them are considered.