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Riordan matrices in the reciprocation of quadratic polynomials

✍ Scribed by Ana Luzón; Manuel A. Morón

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
203 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

Banach's fixed point theorem Reciprocal of a quadratic polynomial Riordan matrices Changes of variables

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 the structure 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.

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