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

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

    and    

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

approximates Euler's constant with an error less than

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