Generalized Neutrino Mixing from the Atmospheric Anomaly

We determine the neutrino mixing and mass parameters that are allowed by the Super-Kamiokande atmospheric neutrino data in a three-neutrino model with one mass-squared difference contributing to the oscillations. We find that although $\nu_\mu\to\nu_\tau$ oscillations are favored, $\nu_\mu\to \nu_e$ oscillations with amplitude as large as 0.18 are allowed even after accounting for the limit from the CHOOZ reactor experiment. The range of allowed parameters permit observable $\nu_\mu\leftrightarrow\nu_e$ and $\nu_e\to\nu_\tau$ oscillations in future long-baseline experiments.