New identities in the Catalan triangle.
- Gutiérrez, J.M. 1
- Hernández, M.A. 1
- Miana, P.J. 2
- Romero, N. 1
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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ISSN: 0022-247X
Argitalpen urtea: 2008
Alea: 341
Zenbakia: 1
Orrialdeak: 52-61
Mota: Artikulua
Beste argitalpen batzuk: Journal of Mathematical Analysis and Applications
Lotura duten proiektuak
Laburpena
In this paper we prove new identities in the Catalan triangle whose (n, p) entry is defined byB n, p : = frac(p, n) ((2 n; n - p)), n, p ∈ N, p ≤ n . In fact, we show some new identities involving the well-known Catalan numbers, and specially the identityunderover(∑, p = 1, i) B n, p B n, n + p - i (n + 2 p - i) = (n + 1) C n ((2 (n - 1); i - 1)), i ≤ n, that appears in a problem related with the dynamical behavior of a family of iterative methods applied to quadratic polynomials. © 2007 Elsevier Inc. All rights reserved.