The curve has asymptotes for x = 1 and y = 0.
It has two parts, the left side in the picture is to be seen in quantum mechanics. Given a set of harmonic oscillators, the proportion of the amount in quantum state n+1 to the amount in state n - as function of the temperature - is given by the curve ¹⁾.

The right side can be found (as inverse), for the density of primes ²⁾.

The function is also called the modified exponential function.

Its inverse is the reciprocal logarithm.

notes

1) Kittel 1976 p.128.

2) y = 1 / ln(n), Blij 1990 p.14.