Exact Probability with Perturbative Form for nu_mu -> nu_e Oscillations in Matter of Constant Density

We give an exact expression for the appearance probability P(nu_mu -> nu_e) describing neutrino oscillations in matter of constant density, derived using textbook quantum mechanics stratagems. Our formulation retains the clarity of an expansion in alpha = Delta m_{21}^2/Delta m_{31}^2 and sin2theta_{13} exhibited by the popular Cervera et al. formula [Nucl. Phys. B {\bf 579}, 17 (2000)] while providing greater precision for analytic evaluation of terrestrial oscillation baselines of thousands of kilometers.