  In position dependent mass (PDM) problems, the quantum dynamics of the
associated systems have been understood well in the literature for particular
orderings. However, no efforts seem to have been made to solve such PDM
problems for general orderings to obtain a global picture. In this connection,
we here consider the general ordered quantum Hamiltonian of an interesting
position dependent mass problem, namely the Mathews-Lakshmanan oscillator, and
try to solve the quantum problem for all possible orderings including Hermitian
and non-Hermitian ones. The other interesting point in our study is that for
all possible orderings, although the Schr\"odinger equation of this
Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre
differential equation, their eigenfunctions cannot be represented in terms of
the associated Legendre polynomials with integral degree and order. Rather the
eigenfunctions are represented in terms of associated Legendre polynomials with
non-integral degree and order. We here explore such polynomials and represent
the discrete and continuum states of the system. We also exploit the connection
between associated Legendre polynomials with non-integral degree with other
orthogonal polynomials such as Jacobi and Gegenbauer polynomials.
