  We propose a functional form for the IMF, the L_3 IMF, which is a natural
heavy-tailed approximation to the log-normal distribution. It is composed of a
low-mass power law and a high mass power-law which are smoothly joined
together. Three parameters are needed to achieve this. The standard IMFs of
Kroupa-2001a, Kroupa-2002a and Chabrier-2003b (single stars or systems) are
essentially indistinguishable from this form. Compared to other 3-parameter
functions of the IMF, the L_3 IMF has the advantage that the cumulative
distribution function and many other characteristic quantities have a closed
form, the mass generating function, for example, can be written down
explicitly.
