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