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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