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The Askey-Wilson Function Transform Scheme

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Special Functions 2000: Current Perspective and Future Directions

Part of the book series: NATO Science Series ((NAII,volume 30))

Abstract

In this paper we present an addition to Askey’s scheme of q- hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function. The generalized orthogonality relations and the second order q-differenee equations for these families are given. Limit transitions between these families are discussed. The quantum group theoretic interpretations are discussed shortly.

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Author information

Authors and Affiliations

  1. Technische Universiteit Delft, Fac. ITS, Afd. TWA, Postbus 5031, 2600 GA, Delft, The Netherlands

    Erik Koelink

  2. Universiteit van Amsterdam, KdV Institute for Mathematics, Pl. Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Jasper V. Stokman

Authors
  1. Jasper V. Stokman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Arizona State University, Tempe, Arizona, USA

    Joaquin Bustoz  & Sergei K. Suslov  & 

  2. Department of Mathematics, University of South Florida, Tampa, Florida, USA

    Mourad E. H. Ismail

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Koelink, E., Stokman, J.V. (2001). The Askey-Wilson Function Transform Scheme. In: Bustoz, J., Ismail, M.E.H., Suslov, S.K. (eds) Special Functions 2000: Current Perspective and Future Directions. NATO Science Series, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0818-1_9

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  • DOI: https://doi.org/10.1007/978-94-010-0818-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7120-5

  • Online ISBN: 978-94-010-0818-1

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