Correlation energy of the spin-polarized uniform electron gas at high density

The correlation energy per electron in the high-density uniform electron gas can be written as E-c(r(s),zeta) = lambda(0)(zeta) 1n r(s) + epsilon(0)(zeta) + lambda(1)(zeta) r(s) 1n r(s) + O(r(s)), where r(s) is the Seitz radius and zeta is the relative spin polarization. We derive an expression for lambda(1)(zeta) that is exact for any zeta, including the paramagnetic and ferromagnetic limits lambda(1)(0) and lambda(1)(1), and discover that the previously published lambda(1)(1) value is incorrect. We trace this error to an integration and limit that do not commute. The spin resolution of lambda(1)(zeta) into contributions of electron pairs is also derived.