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Orthogonal polynomials and laurent polynomials related to the Hahn-Extonq-Bessel function

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Abstract

Laurent polynomials related to the Hahn-Extonq-Bessel function, which areq-analogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurentq-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orthogonal polynomials, the orthogonality measure is determined using the three-term recurrence relation as a starting point. The relation between Chebyshev polynomials of the second kind and the Laurentq-Lommel polynomials and related functions is used to obtain estimates for the latter.

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Authors and Affiliations

  1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, NL-1018 TV, Amsterdam, The Netherlands

    H. T. Koelink

  2. Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001, Leuven (Heverlee), Belgium

    W. Van Assche

Authors
  1. H. T. Koelink
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  2. W. Van Assche
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Koelink, H.T., Van Assche, W. Orthogonal polynomials and laurent polynomials related to the Hahn-Extonq-Bessel function. Constr. Approx 11, 477–512 (1995). https://doi.org/10.1007/BF01208433

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  • DOI: https://doi.org/10.1007/BF01208433

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