  The well-known Carnahan-Starling (CS) equation of state (EoS) [1] for the
hard sphere (HS) fluid was derived from a quadratic relation between the
integer portions of the virial coefficients, Bn, and their orders, n. Here we
extend the method to the full virial coefficients Bn for the general
D-dimensional case. We assume a polynomial function of (D-1)th order for the
virial coefficients starting from n=4 and EoS are derived from it. For the hard
rob (D=1) case, the exact solution is obtained. For the stable hard disk fluid
(D=2), the most recent virial coefficients up to the 10th [2] and accurate
compressibility data[3,4] are employed to construct and test the EoS. For the
stable hard sphere (D=3) fluid, a new CS-type EoS is constructed and tested
with the most recent virial coefficients [5,2] up to the 11th and with the
highly-accurate simulation data for compressibility [6-8]. The simple new EoS
turn out to be as accurate as the highest-level Pade approximations based on
all available virial coefficients, and significantly improve the CS-type EoS in
the hard sphere case. We also shown that as long as the virial coefficients
obey a polynomial function any EoS derived from it will diverge at the
non-physical packing fraction=1.
