The relation between the sérsic law shape along major and minor axes of elliptical galaxies

In this paper we discuss the reason for the widely found discrepancy between Sérsic brightness law fitted along major and minor axes of elliptical galaxies. We show that this difference is a natural consequence of the isophotes eccentricity law. We present a mathematical transformation that allows to obtain the minor axis Sérsic's law from that of the mayor axis one, provided that the eccentricity can be represented by a well behaved, though very general, function of the radius, and that the isophotes ellipses major axis are aligned and concentric. For constant eccentricity, only the coefficient of R1/n is changed, while for distance dependent eccentricity the transformation is given by the Lerch F transcendental function. We discuss 28 galaxies of type E0 to E7, dS0 and S0.