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3.5: Gases of weakly interacting particles
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/03%3A_Ideal_and_Not-So-Ideal_Gases/3.05%3A_Gases_of_weakly_interacting_particles
The second of these relations enables the calculation of the $3^{rd}$ virial coefficient $C(T)$ . (Let me leave the calculation of $J_3$ and $C(T)$ , for the hardball model, for the reader's exe...The second of these relations enables the calculation of the $3^{rd}$ virial coefficient $C(T)$ . (Let me leave the calculation of $J_3$ and $C(T)$ , for the hardball model, for the reader's exercise.) Evidently, a more complete solution of Eqs. ( $\ref{114}$ ), ( $\ref{116}$ ), and ( $\ref{117}$ ) may be used to calculate an arbitrary virial coefficient, though starting from the $5^{th}$ coefficient, such calculations may be completed only numerically even in the simplest hardball model.

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