Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-15T07:05:01.401Z Has data issue: false hasContentIssue false

Summability Tests for Singular Points

Published online by Cambridge University Press:  20 November 2018

F. W. Hartmann*
Affiliation:
Villanova University, Villanova, Pennsylvania
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.

King [5] devised two tests for determining when z = 1 is a singular point of the function f(z) defined by

1

having radius of convergence equal to one. The point z = 1 and radius of convergence one may be chosen without loss of generality.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Agnew, R. P., Euler transformation, Amer. J. Math. 66 (1944), 318-338.Google Scholar
2. Bajsanski, B., Sur une classe générale de procédés de sommations du type D'Euler-Borel, Publ. Inst. Math. (Beograd) 10 (1956), 131-152.Google Scholar
3. Cowling, V. F., Summability and analytic continuation, Proc. Amer. Math. Soc. 1 (1950), 536-542.Google Scholar
4. Hille, Einar, Analytic function theory, Vol. II, Ginn & Co., New York, 1961.Google Scholar
5. King, J. P., Tests for singular points, Amer. Math. Monthly, 72 (1965), 870-873.Google Scholar
6. Knopp, K., Theory of functions, Part 1, Dover, New York (1945), p. 83.Google Scholar
7. Sledd, W. T., On the relative strength of Karamata matrices, Illinois J. Math. 15 (1971), 197-202.Google Scholar
8. Titchmarsh, E. C., The theory of functions, Oxford Univ. Press, London, 1952.Google Scholar
9. Vermes, P., Series to series transformations and analytic continuation by matrix methods, Amer. J. Math. 71 (1949), 541-562.Google Scholar