  We solve an eigenvalue equation that appears in several papers about a wide
range of physical problems. The Frobenius method leads to a three-term
recurrence relation for the coefficients of the power series that, under
suitable truncation, yields exact analytical eigenvalues and eigenfunctions for
particular values of a model parameter. From these solutions some researchers
have derived a variety of predictions like allowed angular frequencies, allowed
field intensities and the like. We also solve the eigenvalue equation
numerically by means of the variational Rayleigh-Ritz method and compare the
resulting eigenvalues with those provided by the truncation condition. In this
way we prove that those physical predictions are merely artifacts of the
truncation condition.
