Some results on the Apostol–Bernoulli and Apostol–Euler polynomials

The main object of this paper is to investigate the Apostol–Bernoulli polynomials and the Apostol–Euler polynomials. We first establish two relationships between the generalized Apostol–Bernoulli and Apostol–Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol–Bernoulli polynomials and of the Apostol–Euler polynomials.