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Real orthogonalizing weights for Bessel polynomials. (English) Zbl 0792.33009
The authors continue work on the real orthogonalizing weight for the generalized Bessel polynomials, see {\it K. H. Kwon}, {\it S. S. Kim} and {\it 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 $\langle g,x\sp n \rangle=0)$ already given by Stieltjes, their result is in the form $d \mu\sb \alpha (x)=w\sb \alpha (x)dx$ with $$w\sb \alpha (x)=x\sp \alpha \exp \left( {-2 \over x} \right) \int\sb x\sp \infty t\sp{-\alpha-2} g(t) \exp \left( {2 \over t} \right) dt\ (x>0),$$ and zero for $x \le 0$, under the condition $\int\sb 0\sp \infty w\sb \alpha (x)dx \ne 0$; this condition is satisfied for at least the choices $\alpha=0,\pm 1$.

33C45Orthogonal polynomials and functions of hypergeometric type
Full Text: DOI
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