Real orthogonalizing weights for Bessel polynomials (Q1318388)

The authors continue work on the real orthogonalizing weight for the generalized Bessel polynomials, see \textit{K. H. Kwon}, \textit{S. S. Kim} and \textit{S. S. Han} [Orthogonalizing weights of Tchebychev sets of polynomials [Bull. Lond. Math. Soc. 24, No. 4, 361-367 (1992; Zbl 0768.33007)]. Using `polynomial killers' \(g\) (i.e. a distribution \(g\) having moments \(\langle g,x^ n \rangle=0)\) already given by Stieltjes, their result is in the form \(d \mu_ \alpha (x)=w_ \alpha (x)dx\) with \[ w_ \alpha (x)=x^ \alpha \exp \left( {-2 \over x} \right) \int_ x^ \infty t^{-\alpha-2} g(t) \exp \left( {2 \over t} \right) dt\;(x>0), \] and zero for \(x \leq 0\), under the condition \(\int_ 0^ \infty w_ \alpha (x)dx \neq 0\); this condition is satisfied for at least the choices \(\alpha=0,\pm 1\).