Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit

TL;DR

This paper derives explicit difference equations for Heckman-Opdam hypergeometric functions and their confluent limits, connecting special functions with quantum integrable systems.

Contribution

It introduces explicit difference equations for Heckman-Opdam hypergeometric functions and their confluent Whittaker limits, linking special functions to quantum Toda chains.

Findings

Explicit difference equation for Heckman-Opdam hypergeometric function

Derived difference equation for Whittaker function via confluent limit

Connections established between special functions and quantum integrable models

Abstract

We present an explicit difference equation for the Heckman-Opdam hypergeometric function associated with root systems. Via a confluent hypergeometric limit, an analogous difference equation is obtained for the class-one Whittaker function diagonalizing the open quantum Toda chain.