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Zbl 0664.33001
Habsieger, Laurent
Une q-intégrale de Selberg et Askey. (q-integral of Selberg and Askey). (French)
[J] SIAM J. Math. Anal. 19, No.6, 1475-1489 (1988). ISSN 0036-1410; ISSN 1095-7154/e

The multi-dimensional beta integral evaluation given by Selberg has been shown to be equivalent to, and thus imply, a root system conjecture made by {\it I. G. Macdonald} [SIAM J. Math. Anal. 13, 988-1007 (1982; Zbl 0498.17006)]. {\it R. Askey} [SIAM J. Math. Anal. 11, 938-951 (1980; Zbl 0458.33002)] conjectured a q-analog of the Selberg integral, motivated at least in part by the existence of q-analogs by Andrews, Macdonald, and Morris of the Macdonald conjecture. \par The author proves the Askey conjecture, following the outline of Selberg's original proof, with some clever analytical arguments at points where Selberg's arguments from symmetry break down. He also applies the evaluation of the Askey integral to proving a conjecture by Morris for the root system $A\sb n$.
[D.M.Bressoud]

MSC 2000:: *33B15 Gamma-functions, etc.
33C80 Connections of theory of special functions with groups and algebras
05A19 Combinatorial identities

Keywords: q-analog of the Selberg integral; Macdonald conjecture

Citations: Zbl 0498.17006; Zbl 0458.33002

Cited in: Zbl 1002.33011 Zbl 0989.33001 Zbl 0693.05009

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