A note on the summation of divergent power series
- 1 July 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 66 (1) , 109-114
- https://doi.org/10.1017/s0305004100044765
Abstract
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.Keywords
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