Euler-Gompertz constant

The Euler-Gompertz constant is the value of the continued fractionDlmfMathworldPlanetmath


in which after three appearances of 1 in the numerator position, follow the integers from 2 forward each given twice consecutively; the value of this constant is approximately 0.596347362323194074341078499369279376074… Finch gives two formulas for this constant:


with e being the natural log base and Ei being the exponential integralDlmfDlmfDlmfMathworldPlanetmath.

The constant can also be expressed as a formula involving an infinite sum:


with γ being the Euler-Mascheroni constant.


  • 1 Steven R. Finch, Mathematical Constants. Cambridge: Cambridge University Press (2003): 424
Title Euler-Gompertz constant
Canonical name EulerGompertzConstant
Date of creation 2013-03-22 18:49:06
Last modified on 2013-03-22 18:49:06
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A55
Synonym Gompertz constant