The hypergeometric function for the root system of type $A$ with a certain degenerate parameter

TL;DR

This paper explicitly expresses the Heckman-Opdam hypergeometric function for type A root systems with a specific degenerate parameter using Lauricella hypergeometric functions, providing a new analytical representation.

Contribution

It introduces an explicit formula linking Heckman-Opdam and Lauricella hypergeometric functions for a special degenerate case in type A root systems.

Findings

Explicit expression for Heckman-Opdam hypergeometric function in terms of Lauricella functions.

New analytical tools for studying hypergeometric functions associated with root systems.

Potential applications in representation theory and special functions.

Abstract

We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function.