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

T. S. Chihara

doi:10.4153/CMB-1970-098-7

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In his classic memoir on the moment problem that bears his name, Stieltjes [2] exhibited

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.

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

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Christiansen, Jacob Stordal 2003. The moment problem associated with the Stieltjes–Wigert polynomials. Journal of Mathematical Analysis and Applications, Vol. 277, Issue. 1, p. 218.

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de Haro, Sebastian and Tierz, Miguel 2005. Discrete and oscillatory matrix models in Chern–Simons theory. Nuclear Physics B, Vol. 731, Issue. 3, p. 225.

Christiansen, Jacob S. and Koelink, Erik 2006. Self-adjoint difference operators and classical solutions to the Stieltjes–Wigert moment problem. Journal of Approximation Theory, Vol. 140, Issue. 1, p. 1.

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

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