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http://dx.doi.org/10.4134/CKMS.c190098

MORE EXPANSION FORMULAS FOR q, 𝜔-APOSTOL BERNOULLI AND EULER POLYNOMIALS  

Ernst, Thomas (Department of Mathematics Uppsala University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 417-445 More about this Journal
Abstract
The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 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 polynomial;
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