Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial

TL;DR

This paper derives a Rodrigues formula for nonsymmetric multivariable Laguerre polynomials, enabling algebraic generation of these polynomials for the $B_N$-type Calogero model with distinguishable particles.

Contribution

It introduces a novel Rodrigues formula for nonsymmetric multivariable Laguerre polynomials, expanding the algebraic tools available for these orthogonal polynomials.

Findings

First algebraic generation of all nonsymmetric multivariable Laguerre polynomials with variable-specific parities

Extension of Takamura and Takano's method to new polynomial class

Facilitates further analytical studies of the $B_N$-type Calogero model

Abstract

Extending a method developed by Takamura and Takano, we present the Rodrigues formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for the $B_{N}$-type Calogero model with distinguishable particles. Our construction makes it possible for the first time to algebraically generate all the nonsymmetric multivariable Laguerre polynomials with different parities for each variable.