Summation of series of positive terms by condensation transformations.

Author:
James W. Daniel

Journal:
Math. Comp. **23** (1969), 91-96

MSC:
Primary 65.10

DOI:
https://doi.org/10.1090/S0025-5718-1969-0238462-6

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 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 are more easily summed than the original and may in fact be transformed further if desired. Numerical examples reveal the power of the method.

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0238462-6

Article copyright:
© Copyright 1969
American Mathematical Society