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Density functional theory as proposed by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] is used to study hard sphere mixture exposed by cylindrically symmetric external field. Exploiting the symmetry of the system, explicit formulas for the weighted densities are derived. The resulting density profiles are compared with new grand canonical Monte Carlo simulations. The comparison reveals very good agreement between the predicted and simulated results even at high densities and very narrow pores. Finally, simple algorithms for computing complete elliptic functions of the first and second kinds that occur in the derived formulae are presented to make the paper self-contained. [ABSTRACT FROM AUTHOR]