Uniform asymptotics for orthogonal polynomials with exponential weight on the positive real axis

Dai, Dao‐Qing; Qiu, Weiyuan; Wang, Jun

doi:10.3233/asy-141219

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…[10,33]; for the measures with the support being a half-line, see e.g. [3,6,7,68,69]; and for discrete measures, see e.g. the monograph [67].…”

Section: Introductionmentioning

confidence: 99%

Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case

Świderski,

Trojan

2024

Annales De l'Institut Fourier

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We study orthogonal polynomials with periodically modulated recurrence coefficients when 0 lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Additionally, we provide the constructive formula for the density in terms of Turán determinants. Moreover, we determine the exact asymptotic behavior of the orthogonal polynomials. Finally, we study scaling limits of the Christoffel-Darboux kernel.Résumé. -Nous étudions des polynômes orthogonaux avec coefficients de récurrence périodiquement modulés, lorsque 0 est une véritable extrémité du spectre de la matrice de Jacobi périodique correspondante. En particulier, nous montrons que leur mesure d'orthogonalité est purement absolument continue sur une demidroite réelle et purement discrète sur son complémentaire. De plus, nous fournissons une formule constructive pour la densité, en termes de déterminants de Turán. Nous déterminons aussi le comportement asymptotique exact des polynômes orthogonaux. Enfin, nous étudions les limites d'échelle du noyau de Christoffel-Darboux. the moments Rx n dµ(x) are finite.

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“…[10,33]; for the measures with the support being a half-line, see e.g. [3,6,7,68,69]; and for discrete measures, see e.g. the monograph [67].…”

Section: Introductionmentioning

confidence: 99%

Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case

Świderski,

Trojan

2024

Annales De l'Institut Fourier

View full text Add to dashboard Cite

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Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions

2018

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Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials L(α) n (x), as well as complementary confluent hypergeometric functions. The expansions are valid for n large and α small or large, uniformly for unbounded real and complex values of x. The new expansions extend the range of computability of L (α) n (x) compared to previous expansions, in particular with respect to higher terms and large values of α. Numerical evidence of their accuracy for real and complex values of x is provided.

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Uniform asymptotics for orthogonal polynomials with exponential weight on the positive real axis

Cited by 2 publications

References 23 publications

Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case

Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case

Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions

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