Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-29T16:03:19.991Z Has data issue: false hasContentIssue false
  • English
  • Français

Orthogonal Polynomials and Hypergeometric Series

Published online by Cambridge University Press:  20 November 2018

A. van der Sluis
A. van der Sluis*
Affiliation:
University of New Brunswick
Rights & Permissions [Opens in a new window]

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 Part I of this paper we present a theory of Padé-approximants for Laurent series, and discuss their relation to orthogonal polynomials. For earlier results in this direction we may refer to (1 ; 7; 8). It is also indicated how this theory can be extended, for example, to matrix polynomials.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 592 - 612
Copyright
Copyright © Canadian Mathematical Society 1958 

Footnotes

Parts I and II of this paper cover parts of a thesis submitted by the author to the University of Amsterdam {General orthogonal polynomials, Groningen, 1956). This paper was completed while the author held a fellowship at the Summer Research Institute of the Canadian Mathematical Congress, Kingston, 1957. The author is greatly indebted to Professors Dr. J. Popken (Amsterdam) and Dr. F. van der Blij (Utrecht) for valuable hints and kind assistance during the preparation of this paper.

References

1. Frank, E., Orthogonality properties of C-fraclions, Bull. Amer. Math. Soc, 55 (1949), 384-390.Google Scholar
2. Hahn, W., Ueber Orthogonalpolynome die q-Differenzen-gleichungen geniigen, Math. Nachr., 2 (1949), 4-34.Google Scholar
3. Krall, H. L., Certain differential equations for Tchebycheff polynomials, Duke Math. J., 4 (1938), 705-718.Google Scholar
4. Krall, H. L. and Frink, O., A new class of orthogonal polynomials: the Bessel polynomials. Trans. Amer. Math. Soc, 65 (1949), 100-115.Google Scholar
5. Padé, H., Récherches sur la convergence des développements en fractions continues d'une certaine catégorie des fonctions,Ann. Sci. Ecole Norm. Sup., 3, 24 (1907), 341-400.Google Scholar
6. Perron, O., Die Lehre von den Kettenbrüchen, 2. Aufl. (Leipzig, 1929).Google Scholar
7. Rossum, Hvan, A theory of orthogonal polynomials based on the Padé-table (Diss. Utrecht, Assen 1953).Google Scholar
8. Rossum, Hvan, Systems of orthogonal and quasi-orthogonal polynomials connected with the Padétable. I, Kon. Ned. Akad. Wet., Proc. Section of Sciences, 58 Ser. A (1955), 517-525; II, idem, 526-534; III, idem, 675-682.Google Scholar
9. Szegö, G., Orthogonal polynomials, A.M.S. Coll. Publ. XXIII (New York, 1939).Google Scholar