The busy function: a new analytic function for describing the integrated
  21-cm spectral profile of galaxies
  Accurate parametrization of galaxies detected in the 21-cm HI emission is of
fundamental importance to the measurement of commonly used indicators of galaxy
evolution, including the Tully-Fisher relation and the HI mass function. Here,
we propose a new analytic function, named the 'busy function', that can be used
to accurately describe the characteristic double-horn HI profile of many
galaxies. The busy function is a continuous, differentiable function that
consists of only two basic functions, the error function, erf(x), and a
polynomial, |x|^n, of degree n >= 2. We present the basic properties of the
busy function and illustrate its great flexibility in fitting a wide range of
HI profiles from the Gaussian profiles of dwarf galaxies to the broad,
asymmetric double-horn profiles of spiral galaxies.
  Applications of the busy function include the accurate and efficient
parametrization of observed HI spectra of galaxies and the construction of
spectral templates for simulations and matched filtering algorithms. We
demonstrate the busy function's power by automatically fitting it to the HI
spectra of 1000 galaxies from the HIPASS Bright Galaxy Catalog, using our own
C/C++ implementation, and comparing the resulting parameters with the
catalogued ones. We also present two methods for determining the uncertainties
of observational parameters derived from the fit.
