Riordan matrices in the reciprocation of quadratic polynomials
type: Item
instance of: scholarly article
title: Riordan matrices in the reciprocation of quadratic polynomials
zbMATH Open document ID: 1175.41029
author: Ana Luzón
author: Manuel A. Morón
published in: Linear Algebra and its Applications
publication date: 2009-04-29T00:00:00Z
review text: The paper deals with two arithmetical triangles: The first are remainders that appear in an iterative process while the second can be interpreted as change of variables. All elements in both type are invertible Riordan arrays (Riordan matrices). In Section 2, the authors develop the theory used in the following sections. In Section 3, the authors compare the remainder of a Taylor expansion with an element of the Riordan group. Finally, they get the Pascal triangle as product of certain matrices. All their remainders are 7-matrices (see (5) from References). In Section 4 the change of variables obtained in Section 3 is studied. In Section 5 some known formulas of the sums of powers of natural numbers are recovered.
Mathematics Subject Classification ID: 41A80
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 5549279
zbMATH Keywords: Banach's fixed point theorem
zbMATH Keywords: reciprocal of a quadratic polynomial
zbMATH Keywords: Riordan matrices
zbMATH Keywords: change of variables
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: j.laa.2008.12.001
OpenAlex ID: W2022187550
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DOI: 10.1016/J.LAA.2008.12.001
description: scientific article; zbMATH DE number 5549279