Integral representations for multiple Hermite and multiple Laguerre polynomials
[Représenta\-tions intégrales pour les polynômes d'Hermite et de Laguerre multiples]
M. BLEHER, Pavel1 ; B.J. Kuijlaars, Arno
1 Indiana University-Purdue University Indianapolis, department of mathematical sciences, 402 N. Blackford St., Indianapolis IN 46202 (USA), Katholieke Universiteit Leuven, department of mathematics, Celestijnenlaan 200 B, 3001 Leuven (Belgique)
Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2001-2014.

On présente des représentations intégrales doubles pour les polynômes d'Hermite et de Laguerre multiples, aussi bien ceux de type I que ceux de type II. On montre aussi la connexion avec les représentations intégrales de certains noyaux de la théorie des matrices aléatoires.

We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.

DOI : 10.5802/aif.2148
Classification : 42C05, 15A52
Keywords: Multiple orthogonal polynomials, random matrices, Christoffel-Darboux formula
Mot clés : polynômes orthogonaux multiples, matrices aléatoires, formule de Christoffel-Darboux
M. BLEHER, Pavel 1 ; B.J. Kuijlaars, Arno 

1 Indiana University-Purdue University Indianapolis, department of mathematical sciences, 402 N. Blackford St., Indianapolis IN 46202 (USA), Katholieke Universiteit Leuven, department of mathematics, Celestijnenlaan 200 B, 3001 Leuven (Belgique) 
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     title = {Integral representations for multiple {Hermite} and multiple {Laguerre} polynomials},
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M. BLEHER, Pavel; B.J. Kuijlaars, Arno. Integral representations for multiple Hermite and multiple Laguerre polynomials. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2001-2014. doi : 10.5802/aif.2148. https://www.numdam.org/articles/10.5802/aif.2148/

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