  We investigate the time dependence of correlation functions in the central
spin model, which describes the electron or hole spin confined in a quantum
dot, interacting with a bath of nuclear spins forming the Overhauser field. For
large baths, a classical description of the model yields quantitatively correct
results. We develop and apply various algorithms in order to capture the
long-time limit of the central spin for bath sizes from 1000 to infinitely many
bath spins. Representing the Overhauser field in terms of orthogonal
polynomials, we show that a carefully reduced set of differential equations is
sufficient to compute the spin correlations of the full problem up to very long
times, for instance up to $10^5\hbar/J_\mathrm{Q}$ where $J_\mathrm{Q}$ is the
natural energy unit of the system. This technical progress renders an analysis
of the model with experimentally relevant parameters possible. We benchmark the
results of the algorithms with exact data for a small number of bath spins and
we predict how the long-time correlations behave for different effective
numbers of bath spins.
