Multiplication formulas for q-Appell polynomials and the multiple q-power sums

Thomas Ernst

Abstract


In the first article on q-analogues of two Appell polynomials, the generalized Apostol-Bernoulli  and Apostol-Euler  polynomials, focus was on generalizations, symmetries, and complementary argument theorems. In this second article, we focus on a recent paper by Luo, and one paper on power sums by Wang and Wang. Most of the proofs are made by using generating functions, and the (multiple) q-addition plays a fundamental role. The introduction of the q-rational numbers in formulas with q-additions enables natural q-extension of vector forms of Raabes multiplication formulas. As special cases, new formulas for q-Bernoulli and q-Euler polynomials are obtained.

Keywords


Raabes multiplication formulas; q-Appell polynomials; multiple q-power sum; symmetry; q-rational number

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References


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DOI: http://dx.doi.org/10.17951/a.2016.70.1.1
Date of publication: 2016-07-04 15:43:59
Date of submission: 2016-06-30 20:36:50


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