Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T19:47:11.021Z Has data issue: false hasContentIssue false
  • English
  • Français

On methods of summability based on integral functions

Published online by Cambridge University Press:  24 October 2008

D. Borwein
D. Borwein
Affiliation:
St Salvator's College University of St Andrews
Get access Rights & Permissions [Opens in a new window]

Extract

Suppose throughout that

and that

is an integral function. Suppose also that l, sn(n = 0,1,…) are arbitrary complex numbers and denote by ρ(ps) the radius of convergence of the series

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 23 - 30
Copyright
Copyright © Cambridge Philosophical Society 1959

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borwein, D.On methods of summability based on power series. Proc. Roy. Soc. Edinb. 64 (1957), 342–49.Google Scholar
(2)Copson, E. T.Functions of a complex variable (Oxford, 1935).Google Scholar
(3)Good, I. J.Relations between methods of summation of series. Proc. Camb. Phil. Soc. 38 (1942), 144–65.CrossRefGoogle Scholar
(4)Hardy, G. H.Orders of infinity (Cambridge, 1910).Google Scholar
(5)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(6)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar
(7)WŁodarski, L.Propriétés des mèthodes continues de limitation du type de Borel. Bull. Acad. Polon. Sci., Cl. III, 4 (1956), 173–75.Google Scholar