An Extended Generalized q-Extensions for the Apostol Type Polynomials

Abstract

Through a modification on the parameters associated with generating function of the q-extensions for the Apostol type polynomials of order α and level m, we obtain some new results related to a unified presentation of the q-analog of the generalized Apostol type polynomials of order α and level m. In addition, we introduce some algebraic and differential properties for the q-analog of the generalized Apostol type polynomials of order α and level m and the relation of these with the q-Stirling numbers of the second kind, the generalized q-Bernoulli polynomials of level m, the generalized q-Apostol type Bernoulli polynomials, the generalized q-Apostol type Euler polynomials, the generalized q-Apostol type Genocchi polynomials of order α and level m, and the q-Bernstein polynomials.