Going beyond closed-form equations

Uhlenbeck and Ford, Lectures in Statistical Mechanics, American Mathematical Society, Providence, 1963, pp. 35-6:

there is the failure of the van der Waals equation to describe the phenomena quantitatively correct [sic], although it is unsurpassed qualitatively. Already in 1901, this failure led Kamerlingh Onnes to abandon all closed expressions for the equation of state and to represent the data by a series expansion of the form:
(3) $\frac{pV}{rT} = 1 + \frac{B(T)}{V} + \frac{C(T)}{V^2} + \cdots$
This is called the virial expansion… The representation (3) was not only desperation, but it contained the insight that the successive deviations from the ideal gas law will give information about the interaction of the molecules in pairs, triples, etc.