The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamical quantities related to classical many-particle systems.

Definition

Consider a system of classical particles interacting through a pair-wise potential

where the bold labels and denote the continuous degrees of freedom associated with the particles e.g.

for spherically symmetric particles and

for rigid non-spherical particles where denotes position and Ω the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as

where β = (k_BT) ^{- 1} the inverse absolute temperature in units of the Boltzmann constant k_B.