A Classical Limit of Noumi's $q$-Integral Operator

TL;DR

This paper shows how a classical Whittaker function integral identity can be derived as a limit case of Noumi's $q$-integral operator related to Macdonald polynomials, connecting quantum and classical integrable systems.

Contribution

It establishes a new link between Macdonald polynomial eigenrelations and classical Whittaker functions through a specific limit process.

Findings

Derivation of Whittaker integral identity from $q$-deformed operators

Connection between Macdonald polynomials and classical special functions

Insight into the classical limit of quantum integrable models

Abstract

We demonstrate how a known Whittaker function integral identity arises from the $t=0$ and $q\to 1$ limit of the Macdonald polynomial eigenrelation satisfied by Noumi's $q$-integral operator.