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XXII.—On Methods of Summability Based on Power Series*

Published online by Cambridge University Press:  14 February 2012

D. Borwein
D. Borwein
Affiliation:
Department of Mathematics, St Salvator's College, University of St Andrews
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Synopsis

Given a power series with real non-negative coefficients and having radius of convergence p, a summability method P is defined as follows:

The main concern of this note is to establish conditions sufficient for one such method to include another.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 64 , Issue 4 , 1957 , pp. 342 - 349
Copyright
Copyright © Royal Society of Edinburgh 1957

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References

Borwein, D., 1957. “On a scale of Abel-type summability methods”, Proc. Camb. Phil. Soc, 53, 318–322.CrossRefGoogle Scholar
Hardy, G. H., 1949. Divergent Series. Oxford.Google Scholar
Hobson, E. W., 1927. The Theory of Functions of a Real Variable, I. Cambridge.Google Scholar
Widder, D. V., 1946. The Laplace Transform. Princeton.Google Scholar