[en] Previous work has considered the validity of the perturbation theory technique of solving the radial differential equation for the collisionless drift wave in a tokamak only near marginal stability for the most unstable radial eigenmode. The present work extends the previous result and determines more exact eigenvalue equations (for all even and odd spatial modes) that are valid for arbitrary growth rates. Away from and perhaps near marginal stability, these more complete eigenvalue equations are required in order to accurately calculate growth rates