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Summability Tests for Singular Points

Published online by Cambridge University Press:  20 November 2018

F. W. Hartmann
F. W. Hartmann*
Affiliation:
Villanova University, Villanova, Pennsylvania
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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
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 525 - 528
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