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Gompertz Constant

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The Gompertz constant is defined by

G=int_0^infty(e^(-u))/(1+u)du
(1)
=-eEi(-1)
(2)
=0.596347362...
(3)

(OEIS A073003), where Ei(x) is the exponential integral. Stieltjes (1894, p. J5), crediting Laguerre, gives the continued fraction representation

G=1/(2-)(1^2)/(4-)(2^2)/(6-)(3^2)/(8-)....
(4)

See also

Exponential Integral

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References

Le Lionnais, F. Les nombres remarquables. Paris, France: Hermann, p. 29, 1983.Sloane, N. J. A. Sequence A073003 in "The On-Line Encyclopedia of Integer Sequences."Stieltjes, T. J. "Recherches sur les fractions continues." Ann. Fac. Sci. Toulouse 8, J1-J122, 1894. https://archive.numdam.org/item/AFST_1894_1_8_4_J1_0/.

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Gompertz Constant

Cite this as:

Weisstein, Eric W. "Gompertz Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GompertzConstant.html

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