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Constructive Approximation

, Volume 27, Issue 1, pp 15–32 | Cite as

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

  • Christian BergEmail author
  • Christophe VignatEmail author
Article

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.

Keywords

Recursion Formula Laguerre Polynomial Inverse Gamma Pochhammer Symbol Inverse Gamma Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100CopenhagenDenmark
  2. 2.Laboratoire d'Informatique IGM, UMR 8049, Universite de Marne-la-Vallee, 5 Bd. Descartes, F-77454Marne-la-Vallee CedexFrance

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