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On Borel-type methods of summability

Published online by Cambridge University Press:  26 February 2010

D. Borwein
D. Borwein
Affiliation:
St. Salvator's College, University of St. Andrews.
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Extract

Suppose throughout that l, an (n = 0, 1, …) are arbitrary complex numbers, that α is a fixed positive number and that x is a variable in the interval [0,µ]. Let

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 128 - 133
Copyright
Copyright © University College London 1958

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References

1.Good, I. J., “Relations between methods of summation of series”, Proc. Camb. Phil. Soc., 38 (1942), 144–165.CrossRefGoogle Scholar
2.Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
3.Hardy, G. H., “On the summability of series by Borel's and Mittag-Leffler's methods”, Journal London Math. Soc., 9 (1934), 153–157.CrossRefGoogle Scholar
4.Wlodarski, L., “Propriétés des méthodes continues de limitation du type de Borel”, Bull. Acad. Polon. Sci., Cl. III, 4 (1956), 173–175.Google Scholar