Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-10T23:45:42.275Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Relation between the Logarithmic and Borel-Type Summability Methods

Published online by Cambridge University Press:  20 November 2018

D. Borwein  and
B. Watson
D. Borwein
Affiliation:
The University of Western Ontario London, Ontario, Canada
B. Watson
Affiliation:
Memorial University of Newfoundland St. John's, Newfoundland, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Suppose throughout that {sn} is a sequence of real numbers, λ > - 1, a > 0, and β is real. Let N be any non-negative integer such that αN + β > l.

We are concerned primarily with the logarithmic summability method L and the Borel-type method (B, α, β). Some known results involve the Abel-type summability method Aγ.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 153 - 159
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Borwein, D., On methods of summability based on power series, Proc. Royal Soc. Edinburgh. 64 (1957), 342-349.Google Scholar
2. Borwein, D., A logarithmic method of summability, Journal London Math. Soc.. 33 (1958), 212-220.Google Scholar
3. Borwein, D. and Watson, B., Tauberian theorems on a scale of Abel-type summability methods, Journal fur die Reine und Angewandte Mathematik. 298 (1978), 1-7.Google Scholar
4. Borwein, D., Tauberian theorems between the logarithmic and Abel-type summability methods, submitted for publication.Google Scholar
5. Hardy, G. H., Divergent Series, Oxford (1949).Google Scholar
6. Shawyer, B. L. R. and Yang, G. S., On the relation between the Abel-type and Borel-type methods of summability, Proc. Amer. Math. Soc.. 26 (1970), 323-328.Google Scholar
7. Shawyer, B. L. R. and Yang, G. S., Tauberian relations between the Abel-type and the Borel-type methods of summability, Manuscripta Math.. 5 (1971), 341-357.Google Scholar