7 research outputs found
Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series
We point out how Banach Fixed Point Theorem, and the Picard successive
approximation methods induced by it, allows us to treat some mathematical
methods in Combinatorics. In particular we get, by this way, a proof and an
iterative algorithm for the Lagrange Inversion Formula.Comment: 17 pages. We extend the results in the previuous version proving
finally the Lagrange Inversion Formula via Banach Fixed Point Theore
Riordan matrices in the reciprocation of quadratic polynomials
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