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A formula for summing divergent series

Published online by Cambridge University Press:  17 February 2009

J. E. Drummond
J. E. Drummond
Affiliation:
Department of Applied Mathematics, School of General Studies, Australian National University, Canberra A.C.T., 2600, Australia.
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Abstract

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A formula is given for assigning sums to divergent series where the ratio of adjacent terms varies slowly along the series. This formula consistş of a weighted average of partial sums and is shown to be a general formula which can be easily calculated using a simple recurrence relation. It appears to be more powerful than a repeated Aitken or Shanks e1 process as long as the transformed series remains divergent and it is also compared with the Padé approximants. It is demonstrated on a factorial series, on a nearly geometric divergent series and for the extrapolation of a velocity formula for small amplitudes of motion.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 2 , December 1975 , pp. 200 - 214
Copyright
Copyright © Australian Mathematical Society 1975

References

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