# Euler’s constant

Euler’s constant $\gamma$ is defined by

 $\gamma=\lim_{n\rightarrow\infty}\;\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+% \cdots+\frac{1}{n}-\ln{n}\right)$

or equivalently

 $\gamma=\lim_{n\rightarrow\infty}\;\sum_{i=1}^{n}\left[\frac{1}{i}-\ln\left(1+% \frac{1}{i}\right)\right]$

Euler’s constant has the value

 $0.57721566490153286060651209008240243104\ldots$

It is related to the gamma function by

 $\gamma=-\Gamma^{\prime}(1)$

It is not known whether $\gamma$ is rational or irrational.

References.

• Chris Caldwell - “Euler’s Constant”, http://primes.utm.edu/glossary/page.php/Gamma.htmlhttp://primes.utm.edu/glossary/page.php/Gamma.html

Title Euler’s constant EulersConstant 2013-03-22 12:18:27 2013-03-22 12:18:27 akrowne (2) akrowne (2) 10 akrowne (2) Definition msc 40A25 Euler-Mascheroni constant Mascheroni constant