Abstract
In this paper, we give the recursion formula (in a more general case) for the linearization coefficients (l(Nk)(Ak)) for Bessel polynomials (qn), mentioned by Berg and Vignat p. 21. (14) (Constr Approx 27:15-32, 2008), in the expansion Ak=(a1,a2,...,ak)R+k with Sigma 1ikai=1 This recursion formula yields, again, the positivity of the coefficients. In addition, in the case when k=3, we give either an explicit formula for l(A3) and we derive a double integral formula via convolution of Student t-densities. As a bonus, two reductions for this double integral are given; the first reduction uses an integral formula given by Atia and Zeng (Ramanujan J 28:211-221, 2012. 10.1007/s11139-011-9348-4), and the second uses the one given by Boros and Moll (J Comput Appl Math 106:361-368, 1999).