Apostol type (p, q)-Frobenius–Eulerian polynomials and numbers

Abstract

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius–Eulerian numbers and polynomials and investigate some of their basic identities and properties including addition theorems, difference equations, derivative properties, recurrence relations. Integral representations, implicit and explicit formulas and relations for the aforementioned polynomials and numbers are also acquired. Furthermore, some relationships for Apostol type (p, q)-Frobenius–Eulerian polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q) -Apostol Euler polynomials, (p, q)-Apostol Genocchi polynomials and Stirling numbers of the second kind are considered.