A $q$-Hankel transform associated to the quantum linking groupoid for the quantum $SU(2)$ and $E(2)$ groups
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3326033