Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials *

Recently, Srivastava and Pintér [1] investigated several interesting properties and relationships involving the classical as well as the generalized (or higher-order) Bernoulli and Euler polynomials. They also showed (among other things) that the main relationship (proven earlier by Cheon [2]) can easily be put in a much more general setting. The main object of the present sequel to these earlier works is to derive several general properties and relationships involving the Apostol-Bernoulli and Apostol-Euler polynomials. Some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the (generalized) Bernoulli and (generalized) Euler polynomials. Other relationships associated with the Stirling numbers of the second kind are also considered.