  An empirical formula for a Shu distribution function that reproduces a thin
disc with exponential surface density to good accuracy is presented. The
formula has two free parameters that specify the functional form of the
velocity dispersion. Conventionally, this requires the use of an iterative
algorithm to produce the correct solution, which is computationally taxing for
applications like Markov Chain Monte Carlo (MCMC) model fitting. The formula
has been shown to work for flat, rising and falling rotation curves.
Application of this methodology to one of the Dehnen distribution functions is
also shown. Finally, an extension of this formula to reproduce velocity
dispersion profiles that are an exponential function of radius is also
presented. Our empirical formula should greatly aid the efficient comparison of
disc models with large stellar surveys or N-body simulations.
