  Analytic results are presented for the probability of detecting an electron
neutrino after passage through a resonant oscillation region. If the electron
neutrino is produced far above the resonance density, this probability is
simply given by $\langle \,P_{\nu_e} \, \rangle \approx \sin^2 \theta_0+
P_\text{x} \cos 2 \theta_0$, where $\theta_0$ is the vacuum mixing angle. The
probability is averaged over the production as well as the detection positions
of the neutrino and $P_\text{x} $ is the Landau-Zener transition probability
between adiabatic states. Finally, this result is applied to resonance
oscillations within the solar interior.
