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Special Matrices

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On the q-Lie group of q-Appell polynomial matrices and related factorizations

Thomas Ernst
Published Online: 2018-03-02 | DOI: https://doi.org/10.1515/spma-2018-0009


In the spirit of our earlier paper [10] and Zhang and Wang [16],we introduce the matrix of multiplicative q-Appell polynomials of order M ∈ 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 ∈ Cq .

Keywords: q-Lie group; multiplicative q-Appell polynomial matrix; commutative ring; q-Pascal functional matrix

MSC 2010: Primary 17B99; Secondary 17B37; 33C80; 15A23


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About the article

Received: 2017-10-10

Accepted: 2018-02-02

Published Online: 2018-03-02

Citation Information: Special Matrices, Volume 6, Issue 1, Pages 93–109, ISSN (Online) 2300-7451, DOI: https://doi.org/10.1515/spma-2018-0009.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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