A Sérsic profile (or Sérsic model or Sérsic law) is an equation describing the relative surface brightness of a galaxy (i.e., a surface brightness profile), stating that the log of the surface brightness falls off exponentially with distance from the center. The Sérsic index is the reciprocal of the exponent: i.e., if the exponent is 1/n, then n is the Sérsic index.
log I(R) ∝ R1/n
R1/n I(R) ∝ e
The Sérsic profile equation is a generalized profile function for which once instance is the de Vaucouleurs' profile (Sérsic profile with an index of 4) and another the exponential profile (index of 1).