A Commuting q-Analogue of the Addition Formula for Disk Polynomials |
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| Authors: | P. G. A. Floris H. T. Koelink |
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| Affiliation: | (1) Afdeling Wiskunde en Informatica Rijksuniversiteit Leiden P.O. Box 9512 2300 RA Leiden The Netherlands floris@wi.leidenuniv.nl , NL;(2) Vakgroep Wiskunde Universiteit van Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam The Netherlands koelink@fwi.uva.nl, NL |
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| Abstract: | Starting from the addition formula for q-disk polynomials, which is an identity in noncommuting variables, we establish a basic analogue in commuting variables of the addition and product formula for disk polynomials. These contain, as limiting cases, the addition and product formula for little q-Legendre polynomials. As q tends to 1 the addition and product formula for disk polynomials are recovered. Date received: September 29, 1995. Date revised: May 20, 1996. |
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| Keywords: | and phrases: q-Disk polynomials Little q-Jacobi polynomials Affine q-Krawtchouk polynomials Addition formula Product formula. AMS Classification: 33D45 33D80. |
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