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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.

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