Gompertz Constant

$$G\equiv\int_0^\infty {e^{-u}\over 1+u}\,du = -e \mathop{\rm ei}\nolimits (-1) = 0.596347362\ldots,$$

where $\mathop{\rm ei}\nolimits (x)$ is the Exponential Integral. Stieltjes showed it has the Continued Fraction representation

$$G={1\over 2-}{1^2\over 4-}{2^2\over 6-}{3^2\over 8-} \cdots.$$

See also Exponential Integral

References

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 29, 1983.