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An Asymptotic Formula for (1 + 1/x)x Based on the Partition Function

Chao-Ping Chen and Junesang Choi
The American Mathematical Monthly
Vol. 121, No. 4 (April 2014), pp. 338-343
DOI: 10.4169/amer.math.monthly.121.04.338
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.04.338
Page Count: 6
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An Asymptotic Formula for (1 + 1/x)x Based on the Partition Function
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Abstract

Abstract We present a method to produce estimations of the natural logarithmic constant e, accurate to as many decimal places as we desire. The method is based on an asymptotic formula for (1 + 1/x)x, which uses the partition function.

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