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Scales of Logarithmic Methods of Summability

Published online by Cambridge University Press:  20 November 2018

D. Borwein  and
R. Phillips
D. Borwein
Affiliation:
The University of Western Ontario, London, Ontario
R. Phillips
Affiliation:
The University of Western Ontario, London, Ontario
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We suppose throughout that p is a non-negative integer, and use the following notations:

where log0x = x for x ≥ e0 = 1, and logn+1x = log(lognx) for x ≥ en+1 = een (n = 0, 1, 2,…);

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 445 - 452
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Borwein, D., On methods of summability based on power series. Proc. Roy. Soc. Ed. 64 (1957) 342–349.Google Scholar
2. Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
3. Ishiguro, K., On the summability methods of logarithmic type. Proc. Japan Acad. 38 (1962) 703–705.Google Scholar
4. Ishiguro, K., A tauberian theorem for (J, pn) summability. Proc. Japan Acad. 40 (1964) 807–812.Google Scholar
5. Phillips, R., A tauberian theorem for a scale of logarithmic methods of summation. Proc. Cambridge Phil. Soc. (to be published).Google Scholar