Abstract
Positivity of the linearization coefficients for Bessel polynomials is proved in a more general case. The proof is based not only on a recursion formula (a formula similar to one given by Berg and Vignat) but also on giving an explicit triple sum formula. Moreover, this triple sum is simplified and a double sum formula for these linearization coefficients is given. In two general cases, this formula reduces indeed to either Atia and Zeng's formula (M. J. Atia and J. Zeng, An explicit formula for the linearization coefficients of Bessel polynomials, Ramanujan J. 28(2) (2012) 211-221, doi: 10.1007/s11139-0119348- 4) or Berg and Vignat's formulas in their proof of the positivity results about these coefficients (C. Berg and C. Vignat, Linearization coefficients of Bessel polynomials and properties of student t-distributions, Constr. Approx. 27 (2008) 15-32).