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For a uniform electron gas of density n= n↑+ n↓= 3/4π r s 3= π k s 6/192 and spin polarization ζ=(n↑-n↓)/n, we study the Fourier transform ρ c (k, r s, ζ) of the correlation hole, as well as the correlation energy ɛ c (r s, ζ)= F 0∞ dk ρ c/π. In the high-density (r s→ 0) limit, we find a simple scaling relation k s ρ c/π g 2→ f (z, ζ), where z= k/gk s, g=[(1+ ζ) 2/3+(1-ζ) 2/3]/2, and f (z, 1)= f (z, 0). The function f (z, ζ) is only weakly ζ dependent, and its small-z expansion-3z/π 2+ 4√ 3 z 2/π 2+... is also the exact small-wave-vector (k→ 0) expansion for any r s or ζ. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Padé representations for ρ c at any k, r s, or ζ, one within and one beyond the random-phase approximation (RPA). We also show that ρ c RPA obeys a generalization of Misawa’s spin-scaling relation for ɛ c RPA, and that the low-density (r s→∞) limit …