Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T08:51:47.644Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the summation of divergent power series

Published online by Cambridge University Press:  24 October 2008

R. E. Scraton
R. E. Scraton
Affiliation:
University of Bradford
Get access Rights & Permissions [Opens in a new window]

Extract

Many mathematical problems which do not yield a closed-form solution admit of a solution in the form of a power series; differential equations are an obvious example. The direct use of this power series is limited to the interior of its circle of convergence, and this places a restriction—often a severe restriction—on its usefulness. The method described in this paper enables this restriction to be alleviated in many cases; it also enables the convergence of a power series within its circle of convergence to be improved. The method is based on the Euler transformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 109 - 114
Copyright
Copyright © Cambridge Philosophical Society 1969

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)Bromwich, T. J. I'A.Introduction to the theory of infinite series (2nd edition), pp. 62–66. (Macmillan and Co; London, 1926).Google Scholar
(2)Hardy, G. H.Divergent series, pp. 178et seq. (Clarendon Press; Oxford, 1949).Google Scholar