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A Classical Limit of Noumi's $q$ -Integral Operator Alexei Borodin a ,
Ivan Corwin bcd ,
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 Institut Henri Poincaré, 11 Rue Pierre et Marie Curie, 75005 Paris, France
d Clay Mathematics Institute, 10 Memorial Blvd. Suite 902, Providence, RI 02903, USA e Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Beauchef 851, Torre Norte, Santiago, Chile 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.
Keywords:
Macdonald polynomials; Whittaker functions.
MSC: 05E05 ;
33D52 ;
33D52 ;
82B23 Received: September 3, 2015 ; in final form
December 1, 2015 ; Published online
December 3, 2015
Language: English
DOI:
10.3842/SIGMA.2015.098
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