no. 6
On the Faraut-Koranyi hypergeometric functions in rank two
[Sur les fonctions hypergéométriques de Faraut-Koranyi en rang deux]
Engliš, Miroslav1 ; Zhang, Genkai
1 Academy of Sciences, Mathematics Institute, Zitna 25, 11567 Prague 1 (Czech Republic), Göteborgs Universitet, Chalmers tekniska högskola, 41296 Göteborg (Sweden)
Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1855-1875.

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.

DOI : 10.5802/aif.2069
Classification : 33D67, 32M15, 33C67
Keywords: Cartan domain, hypergeometric function, partition, spherical polynomial, Jack polynomial
Mot clés : domaine de Cartan, fonction hypergéométrique, partition, polynôme sphérique, polynôme de Jack
Engliš, Miroslav 1 ; Zhang, Genkai 

1 Academy of Sciences, Mathematics Institute, Zitna 25, 11567 Prague 1 (Czech Republic), Göteborgs Universitet, Chalmers tekniska högskola, 41296 Göteborg (Sweden) 
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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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