Generalized Apostol Type Polynomials Based on Twin-Basic Numbers - Duran, Ugur; Acikgoz, Mehmet; Dutta, Hemen (Communications in Mathematics and Applications, 2020)
In this work, we consider a class of new generating function for \((p,q)\)-analog of Apostol type polynomials of order \(α\) including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order \(α\). 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 \(τ\) and the Bernstein polynomials by which we construct diverse correlations including aforementioned polynomials and the \((p,q)\)-gamma function.