Positivity of Turán determinants for orthogonal polynomials

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dc.creatorSzwarc, Ryszard
dc.date2007-10-17
dc.date.accessioned2026-07-07T08:36:58Z
dc.date.available2026-07-07T08:36:58Z
dc.descriptionThe orthogonal polynomials $p_n$ satisfy Turán's inequality if $p_n^2(x)-p_{n-1}(x)p_{n+1}(x)\ge 0$ for $n\ge 1$ and for all $x$ in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Turán's inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the $q$--ultraspherical polynomials.
dc.identifierhttps://arxiv.org/abs/0710.3389
dc.identifierhttp://arxiv.org/abs/0710.3389
dc.identifierin Harmonic Analysis and Hypergroups, (K.A. Ross et al., ed.) Delhi 1995, Birkhauser, Boston-Basel-Berlin, 1997, 165-182
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140249
dc.subjectClassical Analysis and ODEs
dc.subject42C05, 47B39
dc.titlePositivity of Turán determinants for orthogonal polynomials
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