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The standard calculation of the spectrum of density perturbations producedduring inflation assumes (i) |n-1| << 1 and (ii) |dn/dlnk| << |n-1|. Slow-rollpredicts and observations require (i), but neither slow-roll nor observationsrequire (ii). In this paper I derive formulae for the spectrum, spectral index,and running of the spectral index, assuming only (i) and not (ii). I give alarge class of observationally viable examples in which these general slow-rollformulae are accurate but the standard slow-roll formulae for the spectralindex and running are incorrect.Comment: 26 pages, 6 figure

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