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Riordan matrices in the reciprocation of quadratic polynomials

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Luzón, Ana and Morón, Manuel A. (2009) Riordan matrices in the reciprocation of quadratic polynomials. Linear Algebra and its Applications, 430 (8-9). pp. 2254-2270. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379508005673


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Abstract

We iterate contractive one-degree polynomials with coefficients in the ring K[[x]] of formal power series to calculate the reciprocal in K[[x]] of a quadratic polynomial. Doing this we meet thestructure of Riordan array. We interpret certain changes of variable as a Riordan array. We finish the paper by using our techniques to find new ways to get known formulas for the sum of powers of natural numbers involving Stirling and Eulerian numbers.


Item Type:Article
Uncontrolled Keywords:Inverse relations; arrays; involutions; sums; Banach's fixed point theorem; reciprocal of a quadratic polynomial; Riordan matrices; changes of variables
Subjects:Sciences > Mathematics > Algebra
ID Code:15132
Deposited On:08 May 2012 10:35
Last Modified:12 Dec 2018 15:13

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