An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.