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103. [D. 6. b.] Note on the Logarithmic Series

Published online by Cambridge University Press:  03 November 2016

A. C. Dixon
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Abstract

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Type
Mathematical Note
Information
The Mathematical Gazette , Volume 2 , Issue 30 , December 1901 , pp. 111 - 113
Copyright
Copyright © Mathematical Association 1901

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References

* The above proof of the logarithmic series holds only when x is real. We see however that when x is positive the sum of the series A — C, which consists of positive terms, tends to the limit zero as η increases. This will therefore also hold when x is complex, and thus in any case when | x | < 1, but which value is to be taken has to be decided by considerations of continuity.