Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 098, 7 pages      arXiv:1509.00701      https://doi.org/10.3842/SIGMA.2015.098

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

Alexei Borodin a, Ivan Corwin bcd and Daniel Remenik e
a) Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
b) Columbia University, Department of Mathematics, 2990 Broadway, New York, NY 10027, USA
c) Clay Mathematics Institute, 10 Memorial Blvd. Suite 902, Providence, RI 02903, USA
d) Institut Henri Poincaré, 11 Rue Pierre et Marie Curie, 75005 Paris, France
e) Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Beauchef 851, Torre Norte, Santiago, Chile

Received September 03, 2015, in final form December 01, 2015; Published online December 03, 2015

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.

Key words: Macdonald polynomials; Whittaker functions.

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