dc.contributor.author Martínez-Finkelshtein, Andrei dc.contributor.author Sánchez-Lara, J. F. dc.date.accessioned 2012-08-03T08:25:59Z dc.date.available 2012-08-03T08:25:59Z dc.date.issued 2007 dc.identifier.uri http://hdl.handle.net/10835/1635 dc.description.abstract We discuss the asymptotic behavior (as $n\to \infty$) of the entropic integrals $$E_n= - \int_{-1}^1 \log \big(p^2_n(x) \big) p^2_n(x) w(x) d x,$$ and $$F_n = -\int_{-1}^1 \log (p_n^2(x)w(x)) p_n^2(x) w(x) dx,$$ when $w$ is the symmetric Pollaczek weight on $[-1,1]$ with main parameter $\lambda\geq 1$, and $p_n$ is the corresponding orthonormal polynomial of degree $n$. It is well known that $w$ does not belong to the Szeg\H{o} class, which implies in particular that $E_n\to -\infty$. For this sequence we find the first two terms of the asymptotic expansion. Furthermore, we show that $F_n \to \log (\pi)-1$, proving that this universal behavior'' extends beyond the Szeg\H{o} class. The asymptotics of $E_n$ has also a curious interpretation in terms of the mutual energy of two relevant sequences of measures associated with $p_n$'s. es_ES dc.language.iso en es_ES dc.source Journal of Approximation Theory Vol. 145 Nº 1 (2007) es_ES dc.subject Polinomios simétricos Pollaczek es_ES dc.subject Entropía de Shannon es_ES dc.subject Comportamiento asintótico es_ES dc.subject Integrales entrópicas es_ES dc.subject Shannon entropy es_ES dc.subject Symmetric Pollaczek polynomials es_ES dc.subject Asymptotic behavior es_ES dc.subject Entropic integrals es_ES dc.title Shannon entropy of symmetric Pollaczek 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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