Communications of the
Korean Mathematical Society CKMS

The purpose of this article is to continue the study of $q,\omega$-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al.~and Varma et al., with emphasis on $q,\omega$-Apostol Bernoulli and Euler polynomials, Ward-$\omega$ numbers and multiple $q,\omega$-power sums. Like before, the $q,\omega$-module for the alphabet of $q,\omega$-real numbers plays a crucial role, as well as the $q,\omega$-rational numbers and the Ward-$\omega$ numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

Keywords: $q,\omega$-special function, $q,\omega$-Apostol Bernoulli and Euler poly\-nomial

MSC numbers: Primary 33D99; Secondary 05A40