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On several q-specia...
On several q-special matrices, including the q-Bernoulli and q-Euler matrices
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- Ernst, Thomas (author)
- Uppsala universitet,Matematiska institutionen
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(creator_code:org_t)
- ELSEVIER SCIENCE INC, 2018
- 2018
- English.
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In: Linear Algebra and its Applications. - : ELSEVIER SCIENCE INC. - 0024-3795 .- 1873-1856. ; 542, s. 422-440
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
Keyword
- q-Bernoulli matrix
- q-Cauchy matrix
- Bernoulli complementary argument theorem
- q-Appell polynomial
- Arponen polynomial matrix approach
- q-Stirling number
Publication and Content Type
- ref (subject category)
- art (subject category)
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