  We introduce an approximation for the pair distribution function of the
inhomogeneous hard sphere fluid. Our approximation makes use of our recently
published averaged pair distribution function at contact which has been shown
to accurately reproduce the averaged pair distribution function at contact for
inhomogeneous density distributions. This approach achieves greater
computational efficiency than previous approaches by enabling the use of
exclusively fixed-kernel convolutions and thus allowing an implementation using
fast Fourier transforms. We compare results for our pair distribution
approximation with two previously published works and Monte-Carlo simulation,
showing favorable results.
