  The F-statistic, derived by Jaranowski, Krolak & Schutz (1998), is the
optimal (frequentist) statistic for the detection of nearly periodic
gravitational waves from known neutron stars, in the presence of stationary,
Gaussian detector noise. The F-statistic was originally derived for the case of
a single detector, whose noise spectral density was assumed constant in time,
and for a single known neutron star. Here we show how the F-statistic can be
straightforwardly generalized to the cases of 1) a network of detectors with
time-varying noise curves, and 2) a population of known sources. Fortunately,
all the important ingredients that go into our generalized F-statistics are
already calculated in the single-source/single-detector searches that are
currently implemented, e.g., in the LIGO Software Library, so implementation of
optimal multi-detector, multi-source searches should require negligible
additional cost in computational power or software development.
