Gompertz constant
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
 

When Euler studied divergent infinite series, he encountered  via, for example, the above integral representations. Le Lionnais called  the Gompertz constant because of 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 the series representation

 

Gompertz's constant is connected to the Gregory coefficients via the 2013 formula of I. Mező:

External links
 Wolfram MathWorld
 OEIS entry

Notes