Cari\~{n}ena polynomials are Jacobi polynomials

TL;DR

This paper demonstrates that Cari ilde{n}ena orthogonal polynomials are actually Jacobi polynomials and establishes a correspondence between negative and positive curvature cases in two dimensions.

Contribution

It reveals the equivalence of Cari ilde{n}ena and Jacobi polynomials and identifies a natural bijection between curvature cases, specific to two dimensions.

Findings

Cari ilde{n}ena polynomials are Jacobi polynomials

Existence of a bijection between negative and positive curvature cases

Results are specific to the two-dimensional setting

Abstract

We show that the Cari\~{n}ena 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.