In mathematics, the Gompertz constant or Euler-Gompertz constant, denoted by , appears in integral evaluations and as a value of special functions. It is named after B. Gompertz.
It can be defined by the continued fraction
or, alternatively, by
The most frequent appearance of is in the following integrals:
The numerical value of is about
During the studying divergent infinite series Euler met with via, for example, the above integral representations. Le Lionnais called as Gompertz constant by its role in survival analysis.
Identities involving the Gompertz constant
The constant can be expressed by the exponential integral as
Applying the Taylor expansion of we have that
Gompertz's constant is connected to the Gregory coefficients via the 2013 formula of I. Mező:
- ^ Steven R., Finch (2003). Mathematical Constants. Cambridge University Press. pp. 425–426.
- ^ Mező, István (2013). "Gompertz constant, Gregory coefficients and a series of the logarithm function". Journal of Analysis and Number Theory (7): 1–4.