Determinant Representations of Polynomial Sequences of Riordan Type

Abstract EN

In this paper, using the production matrix of a Riordan array, we obtain a recurrence relation for polynomial sequence associated with the Riordan array, and we also show that the general term for the sequence can be expressed as the characteristic polynomial of the principal submatrix of the production matrix.

As applications, a unified determinant expression for the four kinds of Chebyshev polynomials is given.