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

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

V
(
i
,
j
)
where the bold labels
i
and
j
denote the continuous degrees of freedom associated with the particles, e.g.,

i
=
r
i
for spherically symmetric particles and

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

f
(
i
,
j
)
=
e
−
β
V
(
i
,
j
)
−
1
where
β
=
(
k
B
T
)
−
1
the inverse absolute temperature in units of (Temperature times the Boltzmann constant
k
B
)^{−1} .