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On the q-Lie group of q-Appell polynomial matrices and related factorizations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2018 (English)In: Special Matrices, ISSN 2300-7451, Vol. 6, no 1, p. 93-109Article in journal (Refereed) Published
Abstract [en]

In the spirit of our earlier paper [10] and Zhang andWang [16], we introduce the matrix of multiplicative q-Appell polynomials of order M is an element of Z. This is the representation of the respective q-Appell polynomials in ke-ke basis. Based on the fact that the q-Appell polynomials form a commutative ring [11], we prove that this set constitutes a q-Lie group with two dual q-multiplications in the sense of [9]. A comparison with earlier results on q-Pascal matrices gives factorizations according to [7], which are specialized to q-Bernoulli and q-Euler polynomials. We also show that the corresponding q-Bernoulli and q-Euler matrices form q-Lie subgroups. In the limit q -> 1 we obtain corresponding formulas for Appell polynomial matrices. We conclude by presenting the commutative ring of generalized q-Pascal functional matrices, which operates on all functions f is an element of C-q(infinity).

Place, publisher, year, edition, pages
DE GRUYTER POLAND SP ZOO , 2018. Vol. 6, no 1, p. 93-109
Keywords [en]
q-Lie group, multiplicative q-Appell polynomial matrix, commutative ring, q-Pascal functional matrix
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-354534DOI: 10.1515/spma-2018-0009ISI: 000428409400009OAI: oai:DiVA.org:uu-354534DiVA, id: diva2:1234421
Available from: 2018-07-24 Created: 2018-07-24 Last updated: 2018-07-24Bibliographically approved

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