Generalized apostol-type polynomial matrix and its algebraic properties

Abstract

The aim of this paper is to introduce the generalized Apostol-type polynomial matrix W [m−1,α](x;c,a;λ;µ;ν) and the generalized Apos-tol-type matrix W [m−1,α](c,a;λ;µ;ν). Using some properties of the generalized Apostol-type polynomials and numbers, we deduce a product formula for W [m−1,α](x;c,a;λ;µ;ν) and provide some factorizations of the Apostol-type polynomial matrix W [m−1](x;c,a;λ;µ;ν), involving the generalized Pascal matrix, Fibonacci and Lucas matrices, respectively. AMS 2010 Subject Classification: 11B68, 11B83, 11C08, 11B39, 33B99.