Comptes Rendus
no. 2
Mathematical Analysis
Scaled asymptotics for q-orthogonal polynomials
[Asymptotiques dilatés pour q-polynômes orthogonaux]

Présenté par : Philippe G. Ciarlet

Mourad E.H. Ismail1 ; Ruiming Zhang2
1 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
2 School of Mathematics, Guangxi Normal University, Guilin City, Guangxi 541004, PR China
Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 71-75.

Nous résumons des résultats d'un article à venir sur les expansions asymptotiques de Plancherel–Rotach pour les polynômes q−1-Hermite, q-Laguerre et de Stieltjes–Wigert. Le comportement asymptotique est en général chaotique lorsqu'une certaine variable est irrationnelle. Dans le cas rationnel, les termes principaux de l'expansion asymptotique comportent des fonctions théta.

We summarize results of a forthcoming paper on Plancherel–Rotach asymptotic expansions for the q−1-Hermite, q-Laguerre and Stieltjes–Wigert polynomials. The asymptotics in the bulk exhibit chaotic behavior when a certain variable is irrational. In the rational case the main terms in the asymptotic expansion involve theta functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.11.018
Mourad E.H. Ismail 1 ; Ruiming Zhang 2

1 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
2 School of Mathematics, Guangxi Normal University, Guilin City, Guangxi 541004, PR China 
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Mourad E.H. Ismail; Ruiming Zhang. Scaled asymptotics for q-orthogonal polynomials. Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 71-75. doi : 10.1016/j.crma.2006.11.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.018/

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