[Sur les fonctions hypergéométriques de Faraut-Koranyi en rang deux]
Nous donnons une description complète du comportement à la frontière des fonctions hypergéométriques généralisées introduites par Faraut et Koranyi sur les domaines de Cartan de rang deux. Le principal outil est une nouvelle représentation intégrale pour certains polynômes sphériques, qui peut avoir un intérêt dans d'autres contextes.
We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.
Keywords: Cartan domain, hypergeometric function, partition, spherical polynomial, Jack polynomial
Mot clés : domaine de Cartan, fonction hypergéométrique, partition, polynôme sphérique, polynôme de Jack
@article{AIF_2004__54_6_1855_0,
author = {Engli\v{s}, Miroslav and Zhang, Genkai},
title = {On the {Faraut-Koranyi} hypergeometric functions in rank two},
journal = {Annales de l'Institut Fourier},
pages = {1855--1875},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {54},
number = {6},
year = {2004},
doi = {10.5802/aif.2069},
mrnumber = {2134227},
zbl = {1079.33010},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2069/}
}
TY - JOUR AU - Engliš, Miroslav AU - Zhang, Genkai TI - On the Faraut-Koranyi hypergeometric functions in rank two JO - Annales de l'Institut Fourier PY - 2004 SP - 1855 EP - 1875 VL - 54 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2069/ DO - 10.5802/aif.2069 LA - en ID - AIF_2004__54_6_1855_0 ER -
%0 Journal Article %A Engliš, Miroslav %A Zhang, Genkai %T On the Faraut-Koranyi hypergeometric functions in rank two %J Annales de l'Institut Fourier %D 2004 %P 1855-1875 %V 54 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2069/ %R 10.5802/aif.2069 %G en %F AIF_2004__54_6_1855_0
Engliš, Miroslav; Zhang, Genkai. On the Faraut-Koranyi hypergeometric functions in rank two. Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1855-1875. doi : 10.5802/aif.2069. http://www.numdam.org/articles/10.5802/aif.2069/
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