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Accurate parametrization of galaxies detected in the 21-cm HI emission is offundamental importance to the measurement of commonly used indicators of galaxyevolution, including the Tully-Fisher relation and the HI mass function. Here,we propose a new analytic function, named the 'busy function', that can be usedto accurately describe the characteristic double-horn HI profile of manygalaxies. The busy function is a continuous, differentiable function thatconsists of only two basic functions, the error function, erf(x), and apolynomial, |x|^n, of degree n >= 2. We present the basic properties of thebusy function and illustrate its great flexibility in fitting a wide range ofHI 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 efficientparametrization of observed HI spectra of galaxies and the construction ofspectral templates for simulations and matched filtering algorithms. Wedemonstrate the busy function's power by automatically fitting it to the HIspectra of 1000 galaxies from the HIPASS Bright Galaxy Catalog, using our ownC/C++ implementation, and comparing the resulting parameters with thecatalogued ones. We also present two methods for determining the uncertaintiesof observational parameters derived from the fit.

The busy function: a new analytic function for describing the integrated 21-cm spectral profile of galaxies