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Topic
Mercator series
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Overview
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm:
In summation notation,
The series converges to the natural logarithm (shifted by 1) whenever .
History
The series was discovered independently by Johannes Hudde and Isaac Newton. It was first published by Nicholas Mercator, in his 1668 treatise Logarithmotechnia.