A common form is the Schechter Luminosity Function for galaxies (aka Schechter Function, an example of a Galaxy Luminosity Function), a "modified" Power Law providing a format for such functions:
n(x)dx = ΦSunxae-xdx
Some typical values of the plug-in parameters:
Other variations of luminosity functions are Globular Cluster Luminosity Functions, Galaxy Cluster luminosity functions, and luminosity functions of particular Bands, or lines, or the lines of a specific molecule (e.g., Carbon Monoxide).
Luminosity functions also are assumed to evolve, e.g., to vary with Redshift.
Conditional Luminosity Function (CLF)
Initial Mass Function (IMF)