New Derivation of the Second Virial Coefficient

We present a new, completely rigorous way of proving the relation between the second virial coefficient and the $S$ matrix. The method involves the use of the $U_{2,\infty }$ function introduced by Lee and Yang and proceeds in the most straightforward manner. Although difficulties are encountered for virial coefficients of higher order, there is hope that this type of approach might shed some light on the question of the connection between the virial series and the scattering matrix.