An orthogonality relation for multivariable Bessel polynomials

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].

Keywords:

• Bessel polynomials
• multivariable orthogonal polynomials

2000 Mathematics Subject Classification :

• Primary: 33C50

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 5 6 14. 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 .