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

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.

15 pages, minor corrections and references added

References in corpus (3)

• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
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Cited by in corpus (4)

• Hypercomplex Fock States for Discrete Electromagnetic Schrödinger Operators: A Bayesian Probability Perspective
• Bispectral dual difference equations for the quantum Toda chain with boundary perturbations
• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions
• On a ${\mathbb{C}}^2$-valued integral index transform and bilateral hypergeometric series