3_F_2(1) hypergeometric function and quadratic R-matrix algebra

TL;DR

This paper constructs representations of the quadratic R-matrix algebra using difference operators that act on the 3_F_2(1) hypergeometric function and classical orthogonal polynomials, linking algebraic structures with special functions.

Contribution

It introduces a novel representation of the quadratic R-matrix algebra via difference operators acting on hypergeometric functions and orthogonal polynomials.

Findings

Operators act as parameter shifting operators on hypergeometric functions

Connections established between algebra representations and classical orthogonal polynomials

Discussion of the relationship with the factorization method

Abstract

We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter shifting operators on the 3_F_2(1) hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with the factorization method will be discussed.