Approximate integral equations for the pair correlation function and the partial of the pair correlation function with respect to density are derived for a classical fluid. The equations are solved for the hardsphere potential using secondhyphen; and thirdhyphen;order bridge diagrams. Comparisons are made with the thermodynamic results of the Percusndash;Yevick (PY) and the hypernettedhyphen;chain (HNC) integral equations and with the Reendash;Hoover Padeacute;Plpar;3, 3rpar;approximant. Comparisons are also made of the pair correlation function, the direct correlation function, and the partial of the pair correlation function with respect to density at a density ofrgr;Sgr;3thinsp;equals;thinsp;0.8. The results of the integral equations with bridge diagrams are found to improve on the PY and HNC equations.
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