Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-23T21:18:28.828Z 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.

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

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