Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

Abstract

By means of six specific generating functions, we introduce a type of generalized parametric Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials and systematically study their basic properties. As an application of the new polynomials, we use them in computing a new series of Taylor-type.