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dc.contributor.authorAptekarev, A. I.
dc.contributor.authorDehesa, J. S.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorYáñez, R.
dc.date.accessioned2012-08-01T08:45:54Z
dc.date.available2012-08-01T08:45:54Z
dc.date.issued2009
dc.identifier.urihttp://hdl.handle.net/10835/1630
dc.description.abstractLet $p_n$ 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.isoenes_ES
dc.sourceConstructive Approximation Vol. 30 Nº 1 (2009)es_ES
dc.subjectPolinomios ortogonaleses_ES
dc.subjectEntropía de Shannones_ES
dc.subjectChebyshev polinomioses_ES
dc.subjectFórmula Euler–Maclaurines_ES
dc.subjectOrthogonal polynomialses_ES
dc.subjectShannon entropyes_ES
dc.subjectChebyshev polynomialses_ES
dc.subjectEuler–Maclaurin formulaes_ES
dc.titleDiscrete entropies of orthogonal polynomialses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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