Accurate parametrization of galaxies detected in the 21-cm H i  emission is of fundamental importance to the measurement of commonly used indicators of galaxy evolution , including the Tully–Fisher relation and the H i  mass function .
Here , we propose a new analytic function , named the ‘ busy function ’ , that can be used to accurately describe the characteristic double-horn H i  profile of many galaxies .
The busy function is a continuous , differentiable function that consists of only two basic functions , the error function , \mathrm { erf } ( x ) , and a polynomial , |x| ^ { n } , of degree n \geq 2 .
We present the basic properties of the busy function and illustrate its great flexibility in fitting a wide range of H i  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 H i  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 H i  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 .