dc.contributor.author Aptekarev, A. I. dc.contributor.author Dehesa, J. S. dc.contributor.author Martínez-Finkelshtein, Andrei dc.contributor.author Yáñez, R. dc.date.accessioned 2012-08-01T08:45:54Z dc.date.available 2012-08-01T08:45:54Z dc.date.issued 2009 dc.identifier.uri http://hdl.handle.net/10835/1630 dc.description.abstract Let $p_n$ be the $n$-th orthonormal polynomial on the real line, whose zeros are $\lambda_j^{(n)}$, $j=1, ..., n$. Then for each $j=1, ..., n$, $$\vec \Psi_j^2 = (\Psi_{1j}^2, ..., \Psi_{nj}^2)$$ with $$\Psi_{ij}^2= p_{i-1}^2 (\lambda_j^{(n)}) (\sum_{k=0}^{n-1} p_k^2(\lambda_j^{(n)}))^{-1}, \quad i=1, >..., n,$$ defines a discrete probability distribution. The Shannon entropy of the sequence $\{p_n\}$ is consequently defined as $$\mathcal S_{n,j} = -\sum_{i=1}^n \Psi_{ij}^{2} \log (\Psi_{ij}^{2}) .$$ In the case of Chebyshev polynomials of the first and second kinds an explicit and closed formula for $\mathcal S_{n,j}$ is obtained, revealing interesting connections with the number theory. Besides, several results of numerical computations exemplifying the behavior of $\mathcal S_{n,j}$ for other families are also presented. es_ES dc.language.iso en es_ES dc.source Constructive Approximation Vol. 30 Nº 1 (2009) es_ES dc.subject Polinomios ortogonales es_ES dc.subject Entropía de Shannon es_ES dc.subject Chebyshev polinomios es_ES dc.subject Fórmula Euler–Maclaurin es_ES dc.subject Orthogonal polynomials es_ES dc.subject Shannon entropy es_ES dc.subject Chebyshev polynomials es_ES dc.subject Euler–Maclaurin formula es_ES dc.title Discrete entropies of orthogonal polynomials es_ES dc.type info:eu-repo/semantics/article es_ES dc.rights.accessRights info:eu-repo/semantics/openAccess es_ES
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