Branching Rules for Symmetric Hypergeometric Polynomials

TL;DR

This paper derives branching rules for various symmetric hypergeometric orthogonal polynomials by degenerating from a known branching formula for Macdonald-Koornwinder polynomials, expanding understanding of their structure.

Contribution

It introduces new branching rules for Wilson, continuous Hahn, Jacobi, Laguerre, and Hermite polynomials through degeneration of Macdonald-Koornwinder formulas.

Findings

Derived branching rules for multiple polynomial families.

Connected hypergeometric polynomials via degeneration from Macdonald-Koornwinder.

Enhanced understanding of polynomial structure and relationships.

Abstract

Starting from a recently found branching formula for the six-parameter family of symmetric Macdonald-Koornwinder polynomials, we arrive by degeneration at corresponding branching rules for symmetric hypergeometric orthogonal polynomials of Wilson, continuous Hahn, Jacobi, Laguerre, and Hermite type.