Analytical properties of the R^{1/m} law

Abstract

In this paper we describe some analytical properties of the R^{1/m} law proposed by Sersic to categorize the photometric profiles of elliptical galaxies. In particular, we present the full asymptotic expansion for the dimensionless scale factor b(m) that is introduced when referring the profile to the standard effective radius. Surprisingly, our asymptotic analysis turns out to be useful even for values of m as low as unity, thus providing a unified analytical tool for observational and theoretical investigations based on the R^{1/m} law for the entire range of interesting photometric profiles, from spiral to elliptical galaxies.