Abstract
In a recent paper we introduced a multivariable generalization of the Bessel polynomials, depending on one extra parameter, and related to the so-called hyperbolic Calogero–Moser–Sutherland model with external Morse potential. In this paper, we obtain a corresponding multivariable generalization of a well-known orthogonality relation for the (one-variable) Bessel polynomials due to Krall and Frink [H.L. Krall and O. Frink, A new class of orthogonal polynomials: the Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), pp. 100–115].
2000 Mathematics Subject Classification :
Acknowledgements
I would like to thank J.F. van Diejen for an inspiring discussion on orthogonality, and A.N. Sergeev and A.P. Veselov for bringing Okounkov’s binomial formula for the B C n Jacobi polynomials to my attention. I am also grateful to T.H. Koornwinder for pointing out the references Citation5 Citation6 Citation14. The author was supported by the European Union through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-200405652).
Notes
We recall that a subset is dense in the Zariski topology if and only if the zero polynomial is the only polynomial which vanishes on Y .