Defeating divergence

It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago but not well known, by which the sums of series may be calculated arithmetically, no...

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Bibliographic Details
Published in:ChemTexts (Cham) 2017-09, Vol.3 (3), p.1-6, Article 10
Main Authors: Oldham, Keith B., Myland, Jan C.
Format: Article
Language:English
Subjects:
Biochemistry
Chemistry
Chemistry and Materials Science
Chemistry/Food Science
Divergence
Environmental Chemistry
Lecture Text
Mathematical analysis
Series (mathematics)
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Summary:It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago but not well known, by which the sums of series may be calculated arithmetically, notwithstanding the divergence of the series. A powerful example vindicates both methods.
ISSN:2199-3793
2199-3793
DOI:10.1007/s40828-017-0047-7