An orthogonality relation for multivariable Bessel polynomials

TL;DR

This paper extends the orthogonality relations of Bessel polynomials to a multivariable setting, connecting it to the hyperbolic Sutherland model with Morse potential, and introduces a new generalization of these relations.

Contribution

It provides a multivariable generalization of the orthogonality relation for Bessel polynomials, building on recent work on multivariable Bessel polynomials related to integrable models.

Findings

Derived a multivariable orthogonality relation for the generalized Bessel polynomials

Connected the orthogonality to the hyperbolic Sutherland model with Morse potential

Extended classical one-variable results to multivariable case

Abstract

In a recent paper we introduced a multivariable generalisation of the Bessel polynomials, depending on one extra parameter, and related to the so-called hyperbolic Sutherland model with external Morse potential. In this paper we obtain a corresponding multivariable generalisation of a well-known orthogonality relation for the (one-variable) Bessel polynomials due to Krall and Frink.