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Expansion formulas for Apostol type Q-Appell polynomials, and their special cases
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2018 (English)In: Le Matematiche, ISSN 2037-5298, E-ISSN 0373-3505, Vol. 73, no 1, p. 3-24Article in journal (Refereed) Published
Abstract [en]

We present identities of various kinds for generalized q-ApostolBernoulli and Apostol-Euler polynomials and power sums, which resemble q-analogues of formulas from the 2009 paper by Liu and Wang. These formulas are divided into two types: formulas with only q-ApostolBernoulli, and only q-Apostol-Euler polynomials, or so-called mixed formulas, which contain polynomials of both kinds. This can be seen as a logical consequence of the fact that the q-Appell polynomials form a commutative ring. The functional equations for Ward numbers operating on the q-exponential function, as well as symmetry arguments, are essential for many of the proofs. We conclude by finding multiplication formulas for two q-Appell polynomials of general form. This brings us to the q-H polynomials, which were discussed in a previous paper.

Place, publisher, year, edition, pages
UNIV STUDI CATANIA, DIPT MATEMATICA , 2018. Vol. 73, no 1, p. 3-24
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-358346DOI: 10.4418/2018.73.1.1ISI: 000434633200001OAI: oai:DiVA.org:uu-358346DiVA, id: diva2:1242242
Available from: 2018-08-27 Created: 2018-08-27 Last updated: 2018-08-27Bibliographically approved

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CiteExportLink to record
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