Spectrum of density perturbations produced during inflation to leading order in a general slow-roll approximation

The standard calculation of the spectrum of density perturbations produced during inflation assumes (i) parallel ton-1parallel to<1 and (ii) parallel todn/d ln kparallel toP, spectral index n, and running of the spectral index dn/d ln k, assuming only (i) and not (ii). I give a large class of observationally viable examples in which these general slow-roll formulas are accurate but the standard slow-roll formulas for the spectral index and running are incorrect.