Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T05:23:06.089Z Has data issue: false hasContentIssue false
  • English
  • Français

A Tauberian Theorem for a Scale of Logarithmic Methods of Summation

Published online by Cambridge University Press:  20 November 2018

R. Phillips
R. Phillips*
Affiliation:
University of Western Ontario, London, Ontario
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.

We suppose throughout that p is a non-negative integer, and use the following notations:

where (n = 0 , 1 , 2 , … );

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 897 - 902
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Agnew, R. P., Abel transforms and partial sums of Tauberian series, Ann. of Math. 50 (1949), 110–117.Google Scholar
2. Borwein, D., A logarithmic method of summability, J. London Math. Soc. 83 (1958), 212–220.Google Scholar
3. Borwein, D., On methods of summability based on power series, Proc. Roy. Soc. Edinburgh Sect. A 64 (1957), 342–349.Google Scholar
4. Hardy, G. H., Divergent series (Oxford University Press, Oxford, 1949).Google Scholar
5. Ishiguro, K., Tauberian theorems concerning the summability methods of logarithmic type, Proc. Japan Acad. 39 (1963), 156–159.Google Scholar
6. Ishiguro, K., A converse theorem on the summability methods, Proc. Japan Acad. 39 (1963), 38–41.Google Scholar
7. Kwee, B., A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc. 63 (1967), 401–405.Google Scholar
8. Pitt, H. R., Tauberian theorems (Bombay, 1958).Google Scholar