Riordan matrices in the reciprocation of quadratic polynomials

DOI10.1016/j.laa.2008.12.001zbMath1175.41029OpenAlexW2022187550MaRDI QIDQ1014491

Manuel Alonso-Morón, Ana Luzón

Publication date: 29 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.12.001

zbMATH Keywords

change of variablesBanach's fixed point theoremRiordan matricesreciprocal of a quadratic polynomial

Mathematics Subject Classification ID

Related Items (12)

Double parameter recurrences for polynomials in bi-infinite Riordan matrices and some derived identities ⋮ Finite and infinite dimensional Lie group structures on Riordan groups ⋮ A formula to construct all involutions in Riordan matrix groups ⋮ Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series ⋮ Some algebraic structure of the Riordan group ⋮ Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions ⋮ Identities induced by Riordan arrays ⋮ Structural properties of Riordan matrices and extending the matrices ⋮ Self-inverse Sheffer sequences and Riordan involutions ⋮ Recurrence relations for polynomial sequences via Riordan matrices ⋮ Some inverse limit approaches to the Riordan group ⋮ The group generated by Riordan involutions

Cites Work

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• A Catalan triangle
• The umbral calculus
• Pascal triangles, Catalan numbers and renewal arrays
• Riordan arrays and combinatorial sums
• Matrices determined by a linear recurrence relation among entries
• Inverse relations and Schauder bases
• Some summation rules related to the Riordan arrays
• Bijections and the Riordan group
• Decomposition and group theoretic characterization of pairs of inverse relations of the Riordan type
• Simple proofs of open problems about the structure of involutions in the Riordan group
• Riordan group involutions
• Johann Faulhaber and Sums of Powers
• On Some Alternative Characterizations of Riordan Arrays
• The Method of Coefficients
• Some open questions about random walks, involutions, limiting distributions, and generating functions

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