Generalized Apostol Type Polynomials Based on Twin-Basic Numbers

Abstract

In this work, we consider a class of new generating function for (p, q)-analog of Apostol type polynomials of order alpha including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order alpha. By making use of their generating function, we derive some useful identities. We also introduce the generating functions of (p, q)-analogues of the Stirling numbers of second kind of order tau and the Bernstein polynomials by which we construct diverse correlations including aforementioned polynomials and the (p, q)-gamma function.