Applications of Riordan matrix functions to Bernoulli and Euler polynomials

DOI10.1016/j.laa.2016.06.014zbMath1343.05009OpenAlexW2413596607MaRDI QIDQ306446

F. Blanchet-Sadri, M. Dambrine

Publication date: 31 August 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.06.014

zbMATH Keywords

Riordan arrayRiordan groupBernoulli polynomials and numbersconjugate Bernoulli and Euler polynomialsEuler polynomials and numbersPascal matrix

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Theory of matrix inversion and generalized inverses (15A09) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Bernoulli and Euler numbers and polynomials (11B68) Permutations, words, matrices (05A05) Matrices of integers (15B36)

Uses Software

• DLMF

Cites Work

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• Row sums and alternating sums of Riordan arrays
• On an extension of Riordan array and its application in the construction of convolution-type and Abel-type identities
• New identities involving Bernoulli and Euler polynomials
• Sequence characterization of Riordan arrays
• The Riordan group
• An extension of the generalized Pascal matrix and its algebraic properties
• Combinatorial identities in dual sequences
• A note on the Bernoulli and Euler polynomials
• Bijections and the Riordan group
• Some algebraic structure of the Riordan group
• The Sheffer group and the Riordan group
• Simple proofs of open problems about the structure of involutions in the Riordan group
• Riordan group involutions
• The Matrices of Pascal and Other Greats
• A Primer on Bernoulli Numbers and Polynomials
• Pascal Matrices
• Pascal's Matrices
• Some open questions about random walks, involutions, limiting distributions, and generating functions

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