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


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.


Recursion Formula Laguerre Polynomial Inverse Gamma Pochhammer Symbol Inverse Gamma Distribution 
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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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