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A Characterization and a Class of Distribution Functions for the Stieltjes-Wigert Polynomials

Published online by Cambridge University Press:  20 November 2018

T. S. Chihara
T. S. Chihara*
Affiliation:
University of Alberta, Edmonton, Alberta
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In his classic memoir on the moment problem that bears his name, Stieltjes [2] exhibited

1

as an example of an indeterminate (Stieltjes) moment sequence.

Stieltjes also obtained the corresponding S-fraction and thus implicitly obtained the three-term recurrence formula satisfied by the corresponding orthogonal polynomials.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 529 - 532
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Riesz, M., Sur les problèmes des moments et le théorème de Parseval correspondant, Acta Sci. Math. (Szeged) 1 (1922-23), 209-225.Google Scholar
2. Stieltjes, T. J., Recherches sur les fractions continues, Oeuvres, Tome II, Noordhoff, Groningen, 1918. 402-566.Google Scholar
3. Szegö, G. Orthogonal Polynomials, Colloq. Publ., Vol. 23, Amer. Math. Soc., New York, 1939.Google Scholar
4. Wigert, S., Sur les polynomes orthogonaux et l'approximation des fonctions continues. Ark. Mat. Astr. Fys. (18) 17 (1923), 15 pp.Google Scholar