Gauss's Constant
The Reciprocal of the Arithmetic-Geometric Mean of 1 and 
,
 |  |  | (1) |
|  | (2) | |
|  | ||
|  | (3) | |
|  | (4) |
where
is the complete Elliptic Integral of the First Kind and 
is the Gamma Function.See also Arithmetic-Geometric Mean, Gauss-Kuzmin-Wirsing Constant
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/gauss/gauss.html
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