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Unified (p,q)-analog of Aspostol type polynomials of order α

Duran Ugur (Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, İskenderun Technical University, Hatay, Turkey)
Acikgoz Mehmet (Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, Gaziantep, Turkey)
Araci Serkan (Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep, Turkey)

In this work, we introduce a class of a 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 (p,q)-analog of Stirling numbers of second kind of order v by which we construct a relation including aforementioned polynomials.

Keywords: p,q-calculus, Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Apostol-Genocchi polynomials, Stirling numbers of second kind, Generating function, Cauchy product