On the Faraut-Koranyi hypergeometric functions in rank two
[Sur les fonctions hypergéométriques de Faraut-Koranyi en rang deux]
Engliš, Miroslav ; Zhang, Genkai
Annales de l'Institut Fourier, Tome 54 (2004), p. 1855-1875 / Harvested from Numdam
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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.

Publié le : 2004-01-01
DOI : https://doi.org/10.5802/aif.2069
Classification:  33D67,  32M15,  33C67
Mots clés: domaine de Cartan, fonction hypergéométrique, partition, polynôme sphérique, polynôme de Jack 
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     title = {On the Faraut-Koranyi hypergeometric functions in rank two},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {1855-1875},
     doi = {10.5802/aif.2069},
     mrnumber = {2134227},
     zbl = {1079.33010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_6_1855_0}
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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) pp. 1855-1875. doi : 10.5802/aif.2069. http://gdmltest.u-ga.fr/item/AIF_2004__54_6_1855_0/

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