[Asymptotiques dilatés pour q-polynômes orthogonaux]
Nous résumons des résultats d'un article à venir sur les expansions asymptotiques de Plancherel–Rotach pour les polynômes -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 -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.
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@article{CRMATH_2007__344_2_71_0,
author = {Ismail, Mourad E.H. and Zhang, Ruiming},
title = {Scaled asymptotics for \protect\emph{q}-orthogonal polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {71--75},
publisher = {Elsevier},
volume = {344},
number = {2},
year = {2007},
doi = {10.1016/j.crma.2006.11.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.11.018/}
}
TY - JOUR AU - Ismail, Mourad E.H. AU - Zhang, Ruiming TI - Scaled asymptotics for q-orthogonal polynomials JO - Comptes Rendus. Mathématique PY - 2007 SP - 71 EP - 75 VL - 344 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.11.018/ DO - 10.1016/j.crma.2006.11.018 LA - en ID - CRMATH_2007__344_2_71_0 ER -
%0 Journal Article %A Ismail, Mourad E.H. %A Zhang, Ruiming %T Scaled asymptotics for q-orthogonal polynomials %J Comptes Rendus. Mathématique %D 2007 %P 71-75 %V 344 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.11.018/ %R 10.1016/j.crma.2006.11.018 %G en %F CRMATH_2007__344_2_71_0
Ismail, Mourad E.H.; Zhang, Ruiming. Scaled asymptotics for q-orthogonal polynomials. Comptes Rendus. Mathématique, Tome 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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