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Linearization Coefficients of Bessel Polynomials and Properties of Student t-Distributions

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Constructive Approximation Aims and scope

Abstract

We prove positivity results about linearization and connection coefficients for Bessel polynomials. The proof is based on a recursion formula and explicit formulas for the coefficients in special cases. The result implies that the distribution of a finite convex combination of independent Student t-variables with arbitrary odd degrees of freedom has a density which is a finite convex combination of certain Student t-densities with odd degrees of freedom.

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Authors and Affiliations

  1. Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark

    Christian Berg

  2. Laboratoire d'Informatique IGM, UMR 8049, Universite de Marne-la-Vallee, 5 Bd. Descartes, F-77454, Marne-la-Vallee Cedex, France

    Christophe Vignat

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  1. Christian Berg
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  2. Christophe Vignat
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Correspondence to Christian Berg or Christophe Vignat.

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Berg, C., Vignat, C. Linearization Coefficients of Bessel Polynomials and Properties of Student t-Distributions. Constr Approx 27, 15–32 (2008). https://doi.org/10.1007/s00365-006-0643-6

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  • DOI: https://doi.org/10.1007/s00365-006-0643-6

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