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A Commuting q-Analogue of the Addition Formula for Disk Polynomials

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Constructive Approximation Aims and scope

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.

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Authors and Affiliations

  1. Afdeling Wiskunde en Informatica Rijksuniversiteit Leiden , 2300 RA Leiden, P.O. Box 9512, The Netherlands

    P. G. A. Floris

  2. Vakgroep Wiskunde Universiteit van Amsterdam Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands

    H. T. Koelink

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  1. P. G. A. Floris
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  2. H. T. Koelink
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Date received: September 29, 1995. Date revised: May 20, 1996.

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Floris, P., Koelink, H. A Commuting q-Analogue of the Addition Formula for Disk Polynomials. Constr. Approx. 13, 511–535 (1997). https://doi.org/10.1007/s003659900057

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  • DOI: https://doi.org/10.1007/s003659900057

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