Mathematics – Classical Analysis and ODEs
Scientific paper
1996-09-30
Commun. Math. Phys. 188 (1997), 467--497
Mathematics
Classical Analysis and ODEs
AMS-LaTeX v1.2 (with amssymb.sty), 34 pages
Scientific paper
10.1007/s002200050174
Two families (type $A$ and type $B$) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type $A$) and the Laguerre polynomials (type $B$), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl.
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