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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
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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

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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