Commun. Korean Math. Soc. 2020; 35(2): 417-445
Online first article December 18, 2019 Printed April 30, 2020
https://doi.org/10.4134/CKMS.c190098
Copyright © The Korean Mathematical Society.
Thomas Ernst
Uppsala University
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
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