Scale dependent spectral index in slow roll inflation

Recent observations suggest that the spectral index of the primordial perturbations is very close to unity, as expected in models of slow roll inflation. It is still possible for such models to produce spectra which are scale dependent. We present a formula for the spectrum produced by an arbitrary inflaton potential (within the context of slow roll models). This formula explicitly accounts for the possiblity of scale dependence agreeing with previous results when the running is small, but also giving accurate results (as opposed to previous formulas) in the more interesting case when running is non-negligible.