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On several q-special matrices, including the q-Bernoulli and q-Euler matrices
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2018 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 542, p. 422-440Article in journal (Refereed) Published
Abstract [en]

In the spirit of our earlier articles [12,14,11], and our work [13], we define two dual q-Bernoulli polynomials, with corresponding vector and matrix forms. Following Aceto Trigiante [1], the q-L matrix, the indefinite q-integral of the q-Pascal matrix is the link between the q-Cauchy and the q-Bernoulli matrix. The q-analogue of the Bernoulli complementary argument theorem can be expressed in matrix form through the diagonal An matrix. For the q-Euler polynomials corresponding results are obtained. The umbral calculus for generating functions of q-Appell polynomials is shown to be equivalent to a transform method, which maps polynomials to matrices, a true q-analogue of Arponen [6]. This is manifested by the Vein [21] matrix, which occurs as the transform of the q-difference operator. The Aceto Trigiante shifted q-Bernoulli matrix has a simple connection to the q-Bernoulli Arponen matrix through the q-Pascal matrix. We reintroduce certain q-Stirling numbers is an element of 7L(q) from [12], which will be needed for the polynomial matrix definitions.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC , 2018. Vol. 542, p. 422-440
Keyword [en]
q-Bernoulli matrix, q-Cauchy matrix, Bernoulli complementary argument theorem, q-Appell polynomial, Arponen polynomial matrix approach, q-Stirling number
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-347531DOI: 10.1016/j.laa.2017.06.028ISI: 000425197500021OAI: oai:DiVA.org:uu-347531DiVA, id: diva2:1196657
Conference
20th Meeting of the International-Linear-Algebra-Society (ILAS), JUL 11-15, 2016, Univ Leuven, KU Leuven, Leuven, BELARUS
Available from: 2018-04-10 Created: 2018-04-10 Last updated: 2018-04-10Bibliographically approved

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