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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Summation of series of positive terms by condensation transformations.


Author: James W. Daniel
Journal: Math. Comp. 23 (1969), 91-96
MSC: Primary 65.10
MathSciNet review: 0238462
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Abstract: The condensation transformation, which maps series of positive terms into more conveniently summed alternating series, each term $ {v_j}$ of which is itself an infinite series, is discussed with examples. It is shown that for a large class of extremely slowly convergent series (essentially those dominated by the ``logarithmic scale") the series defining the terms $ {v_j}$ are more easily summed than the original and may in fact be transformed further if desired. Numerical examples reveal the power of the method.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0238462-6
PII: S 0025-5718(1969)0238462-6
Article copyright: © Copyright 1969 American Mathematical Society