Gérard de Vaucouleurs (1918-1995) was first to show in 1948 that
this function best fits the galaxy light profiles, with the only
difference that he held \(n\) fixed to a value of 4. 20 years
later in 1968, J. L. Sérsic showed that \(n\) can have a
variety of values and does not necessarily need to be 4. This profile
depends on the effective radius (\(r_e\)) which is defined as the
radius which contains half of the profile brightness (see Profile magnitude). \(I_e\) is the flux at the effective radius. The
Sérsic index \(n\) is used to define the concentration of the
profile within \(r_e\) and \(b_n\) is a constant dependent
on \(n\). MacArthur et al.^{106} show that for
\(n>0.35\), \(b_n\) can be accurately approximated using
this equation:

MacArthur, L. A.,
S. Courteau, and J. A. Holtzman (2003). “Structure of Disk-dominated
Galaxies. I. Bulge/Disk Parameters, Simulations, and Secular
Evolution”. In: ApJ 582, pp. 689—722.