Analytical expressions for the deprojected S\'ersic model - II. General expressions in terms of the Fox H function

Abstract

The S\'ersic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties cannot be expressed using elementary functions or even standard special functions. We present a set of compact and elegant analytical expressions for the luminosity density, cumulative luminosity and potential for the S\'ersic model in terms of the Fox H function for general values of the S\'ersic index. Furthermore, we present explicit series expansions of these quantities and discuss the asymptotic behaviour. Our analysis completes the work of Mazure & Capelato (2002) and Baes & Gentile (2011) and demonstrates the power of the underestimated Fox H function as a tool for analytical work.