On Three General q, w- Apostol Polynomials and their Connection to q, w- Power Sums

Abstract

The purpose of this article is to continue our study of q, ω-special functions, in particular three general q, ω-Apostol polynomials, which contain an extra parameter λ. We find complementary argument theorems, multiplication formulas and recurrence relations for the corresponding numbers. Furthermore, an explicit formula for the multiple alternating q, ω-power sum is found. These formulas are then specialized to q, ω-Apostol-Bernoulli and Euler polynomials.