EulersConstant {EnvStats} | R Documentation |

##
Euler's Constant

### Description

Explanation of Euler's Constant.

### Details

Euler's Constant, here denoted `\epsilon`

, is a real-valued number that can
be defined in several ways. Johnson et al. (1992, p. 5) use the definition:

`\epsilon = \lim_{n \to \infty}[1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} - log(n)]`

and note that it can also be expressed as

`\epsilon = -\Psi(1)`

where `\Psi()`

is the digamma function
(Johnson et al., 1992, p.8).

The value of Euler's Constant, to 10 decimal places, is 0.5772156649.

The expression for the mean of a
Type I extreme value (Gumbel) distribution involves Euler's
constant; hence Euler's constant is used to compute the method of moments
estimators for this distribution (see `eevd`

).

### Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

### References

Johnson, N. L., S. Kotz, and A.W. Kemp. (1992).
*Univariate Discrete Distributions*. Second Edition.
John Wiley and Sons, New York, pp.4-8.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995).
*Continuous Univariate Distributions, Volume 2*.
Second Edition. John Wiley and Sons, New York.

### See Also

Extreme Value Distribution, `eevd`

.

[Package

*EnvStats* version 2.8.1

Index]