  We use the well-known isomorphism between operator algebras and function
spaces equipped with a star product to study the asymptotic properties of
certain matrix sequences in which the matrix dimension $D$ tends to infinity.
Our approach is based on the $su(2)$ coherent states which allow for a
systematic 1/D expansion of the star product. This produces a trace formula for
functions of the matrix sequence elements in the large-$D$ limit which includes
higher order (finite-$D$) corrections. From this a variety of analytic results
pertaining to the asymptotic properties of the density of states, eigenstates
and expectation values associated with the matrix sequence follows. It is shown
how new and existing results in the settings of collective spin systems and
orthogonal polynomial sequences can be readily obtained as special cases. In
particular, this approach allows for the calculation of higher order
corrections to the zero distributions of a large class of orthogonal
polynomials.
