Constructive Approximation

, Volume 27, Issue 1, pp 15–32

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


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

DOI: 10.1007/s00365-006-0643-6

Cite this article as:
Berg, C. & Vignat, C. Constr Approx (2008) 27: 15. doi:10.1007/s00365-006-0643-6


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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