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

T. S. Chihara

doi:10.4153/CMB-1970-098-7

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Chihara, T.S. 1979. On generalized Stieltjes-Wigert and related orthogonal polynomials. Journal of Computational and Applied Mathematics, Vol. 5, Issue. 4, p. 291.

Sánchez-Dehesa, Jesus 1979. On a general system of orthogonal q-polynomials. Journal of Computational and Applied Mathematics, Vol. 5, Issue. 1, p. 37.

Lubinsky, D. S. and Sharif, A. 1983. On the largest zeroes of orthogonal polynomials for certain weights. Mathematics of Computation, Vol. 41, Issue. 163, p. 199.

Van Assche, Walter 1987. The ratio of q-like orthogonal polynomials. Journal of Mathematical Analysis and Applications, Vol. 128, Issue. 2, p. 535.

Askey, Richard 1989. q-Series and Partitions. Vol. 18, Issue. , p. 151.

Al-Salam, W. A. 1990. Orthogonal Polynomials. p. 1.

Van Assche, Walter 1993. Œuvres Complètes Collected Papers. p. 5.

Valent, Galliano 1994. Asymptotic Analysis of Some Associated Orthogonal Polynomials Connected with Elliptic Functions. SIAM Journal on Mathematical Analysis, Vol. 25, Issue. 2, p. 749.

Valent, Galliano and Van Assche, Walter 1995. The impact of Stieltjes' work on continued fractions and orthogonal polynomials: additional material. Journal of Computational and Applied Mathematics, Vol. 65, Issue. 1-3, p. 419.

Valent, Galliano 1996. Exact solutions of some quadratic and quartic birth and death processes and related orthogonal polynomials. Journal of Computational and Applied Mathematics, Vol. 67, Issue. 1, p. 103.

Berg, Christian 1998. On some indeterminate moment problems for measures on a geometric progression. Journal of Computational and Applied Mathematics, Vol. 99, Issue. 1-2, p. 67.

Askey, R. Ismail, M.E.H. and Van Assche, W. 2001. Ted Chihara and his work on orthogonal polynomials. Journal of Computational and Applied Mathematics, Vol. 133, Issue. 1-2, p. 1.

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.

Bertoin, Jean Biane, Philippe and Yor, Marc 2004. Seminar on Stochastic Analysis, Random Fields and Applications IV. p. 45.

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.

Dolivet, Yacine and Tierz, Miguel 2007. Chern-Simons matrix models and Stieltjes-Wigert polynomials. Journal of Mathematical Physics, Vol. 48, Issue. 2,

Pakes, Anthony G. 2007. Structure of Stieltjes classes of moment-equivalent probability laws. Journal of Mathematical Analysis and Applications, Vol. 326, Issue. 2, p. 1268.

Lopez-Garcia, Marcos 2009. Characterization of distributions with the length-bias scaling property. Electronic Communications in Probability, Vol. 14, Issue. none,

López-García, Marcos 2009. Characterization of solutions to the Stieltjes–Wigert moment problem. Statistics & Probability Letters, Vol. 79, Issue. 10, p. 1337.

Download full list

Article contents

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

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests