  Exact analytical, closed-form solutions, expressed in terms of special
functions, are presented for the case of a three-dimensional nonlinear quantum
oscillator with a position dependent mass. This system is the generalization of
the corresponding one-dimensional system, which has been the focus of recent
attention. In contrast to other approaches, we are able to obtain solutions in
terms of special functions, without a reliance upon a Rodrigues-type of
formula. The wave functions of the quantum oscillator have the familiar
spherical harmonic solutions for the angular part. For the s-states of the
system, the radial equation accepts solutions that have been recently found for
the one-dimensional nonlinear quantum oscillator, given in terms of associated
Legendre functions, along with a constant shift in the energy eigenvalues.
Radial solutions are obtained for all angular momentum states, along with the
complete energy spectrum of the bound states.
