Linearization coefficients of Bessel polynomials

2005/06/22 by Christian Berg, Berg, Christian, Christophe Vignat +1
Mathematics · #33C10 #60E05 #FOS: Mathematics #Geometry and complex manifolds #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #math.PR #msc:33C10 #msc:60E05

paper · pdf · doi:10.48550/arxiv.math/0506458

16 pages

arxiv created 2005/06/22 · openalex publication_date 2005/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 convex combination of independent Student-t random variables with arbitrary odd degrees of freedom has a density which is a convex combination of certain Student-t densities with odd degrees of freedom.

Related

• An explicit formula for the linearization coefficients of Bessel polynomials
• An explicit formula for the linearization coefficients of Bessel polynomials II
• A shorter proof of Kanter's Bessel function concentration bound
• Combinatorial orthogonal expansions
• The distribution function for the maximal height of N non-intersecting Bessel paths