Mathematical Analysis
Scaled asymptotics for q-orthogonal polynomials
Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 71-75.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.018
Ismail, Mourad E.H. 1; Zhang, Ruiming 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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Ismail, Mourad E.H.; Zhang, Ruiming. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.11.018/

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