Cariñena polynomials are Jacobi polynomials

2009/02/03 by Christophe Vignat, C. Vignat, Vignat, C. +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math.CA

paper · pdf · doi:10.48550/arxiv.0902.0451

first version

arxiv created 2009/02/03 · openalex publication_date 2009/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Cariñena orthogonal polynomials are Jacobi polynomials; moreover, there exists a natural bijection between the negative and the positive curvature cases. These results hold only in the two dimensional case.

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