A Riordan array approach to Apostol type-Sheffer sequences

Abstract

In this article, the generalized Apostol type-Sheffer sequences are introduced and their properties including the quasi-monomiality, determinant form and series and conjugate representations are derived via Riordan array techniques. The generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi-Sheffer sequences are obtained as their special cases. Certain examples are considered in terms of generalized Apostol Bernoulli-associated Laguerre sequences, generalized Apostol-Euler-Hermite sequences and generalized Apostol-Genocchi-Legendre sequences to give the applications of main results. The numerical results to calculate the zeros and approximate solutions of these sequences are given and their graphical representations are also shown.