# Mayer f-function

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Mayer_f-function
> Markdown URL: https://mediated.wiki/source/Mayer_f-function.md
> Source: https://en.wikipedia.org/wiki/Mayer_f-function
> Source revision: 1167053351
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

The '''Mayer f-function''' is an auxiliary function that often appears in the series expansion of [thermodynamic](/source/thermodynamic) quantities related to classical [many-particle system](/source/many-particle_system)s.<ref name = "mcquarrie">Donald Allan McQuarrie, ''Statistical Mechanics'' ([HarperCollins](/source/HarperCollins), 1976), page 228
</ref> It is named after chemist and physicist [Joseph Edward Mayer](/source/Joseph_Edward_Mayer).

==Definition==
Consider a system of classical particles interacting through a pair-wise potential
:<math>V(\mathbf{i},\mathbf{j})</math>
where the bold labels <math>\mathbf{i}</math> and <math>\mathbf{j}</math> denote the continuous degrees of freedom associated with the particles, e.g., 
:<math>\mathbf{i}=\mathbf{r}_i</math>
for spherically symmetric particles and
:<math>\mathbf{i}=(\mathbf{r}_i,\Omega_i)</math>
for rigid non-spherical particles where <math>\mathbf{r}</math> denotes position and <math>\Omega</math> the orientation parametrized e.g. by [Euler angles](/source/Euler_angles). The Mayer f-function is then defined as
:<math>f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1</math>
where <math>\beta=(k_{B}T)^{-1}</math> the inverse absolute [temperature](/source/temperature) in units of energy<sup>−1</sup> .

==See also==
*[Virial coefficient](/source/Virial_coefficient)
*[Cluster expansion](/source/Cluster_expansion)
*[Excluded volume](/source/Excluded_volume)

==Notes==
{{reflist}}

Category:Special functions

---
Adapted from the Wikipedia article [Mayer f-function](https://en.wikipedia.org/wiki/Mayer_f-function) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Mayer_f-function?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.