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A $ q$-Hankel transform associated to the quantum linking groupoid for the quantum $ SU(2)$ and $ E(2)$ groups


Authors: Kenny De Commer and Erik Koelink
Journal: Proc. Amer. Math. Soc. 143 (2015), 2515-2526
MSC (2010): Primary 33D80, 33D45, 46L65, 81R50
DOI: https://doi.org/10.1090/S0002-9939-2015-12445-8
Published electronically: February 13, 2015
MathSciNet review: 3326033
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Abstract: A $ q$-analogue of Erdélyi's formula for the Hankel transform of the product of Laguerre polynomials is derived using the quantum linking groupoid between the quantum $ SU(2)$ and $ E(2)$ groups. The kernel of the $ q$-Hankel transform is given by the $ {}_1\varphi _1$-$ q$-Bessel function, and then the transform of a product of two Wall polynomials times a $ q$-exponential is calculated as a product of two Wall polynomials times a $ q$-exponential.


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Additional Information

Kenny De Commer
Affiliation: Department of Mathematics, University of Cergy-Pontoise, UMR CNRS 8088, F-95000 Cergy-Pontoise, France
Address at time of publication: Department of Mathematics, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
Email: Kenny.De.Commer@vub.ac.be

Erik Koelink
Affiliation: Radboud Universiteit Nijmegen, IMAPP, FNWI, Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands
Email: e.koelink@math.ru.nl

DOI: https://doi.org/10.1090/S0002-9939-2015-12445-8
Received by editor(s): August 13, 2013
Received by editor(s) in revised form: January 14, 2014
Published electronically: February 13, 2015
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society