Goldie Horton (University of Texas)

A note on the calculation of Euler's constant
American Mathematical Monthly, Vol. 23 (1916), p73.

Euler's constant is usually defined by the relation

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In this note Horton calls attention to the fact that Euler's constant can be calculated to several places of accuracy from an idea used in Cauchy's integral test for a convergent series of positive monotone decreasing terms, namely that both

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approximate the sum of the series with an error less than math equation. Horton uses this to show that

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approximates Euler's constant with an error less than

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