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The "busy function" accurately describes the characteristic double-horn HI profile of many galaxies. Implemented in a C/C++ library and Python module called BF_dist, it 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. BF_dist offers 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, and can be used to parametrize observed HI spectra of galaxies and the construction of spectral templates for simulations and matched filtering algorithms accurately and efficiently.