  We derive a semi-empirical galactic initial mass function (IMF) from
observational constraints. We assume that the star formation rate in a galaxy
can be expressed as the product of the IMF, $\psi (m)$, which is a smooth
function of mass $m$ (in units of \msun), and a time- and space-dependent total
rate of star formation per unit area of galactic disk. The mass dependence of
the proposed IMF is determined by five parameters: the low-mass slope $\gamma$,
the high-mass slope $-\Gamma$, the characteristic mass $m_{ch}$ (which is close
to the mass $m_{\rm peak}$ at which the IMF turns over), and the lower and
upper limits on the mass, $m_l$ (taken to be 0.004) and $m_u$ (taken to be
120). The star formation rate in terms of number of stars per unit area of
galactic disk per unit logarithmic mass interval, is proportional to
$m^{-\Gamma} \left\{1-\exp\left[{-(m/m_{ch})^{\gamma +\Gamma}}\right]\right\}$,
where $\cal N_*$ is the number of stars, $m_l<m<m_u$ is the range of stellar
masses. The values of $\gamma$ and $\emch$ are derived from two integral
constraints: i) the ratio of the number density of stars in the range
$m=0.1-0.6$ to that in the range $m=0.6-0.8$ as inferred from the mass
distribution of field stars in the local neighborhood, and ii) the ratio of the
number of stars in the range $m=0.08 - 1$ to the number of brown dwarfs in the
range $m=0.03-0.08$ in young clusters. The IMF satisfying the above constraints
is characterized by the parameters $\gamma=0.51$ and $\emch=0.35$ (which
corresponds to $m_{\rm peak}=0.27$). This IMF agrees quite well with the
Chabrier (2005) IMF for the entire mass range over which we have compared with
data, but predicts significantly more stars with masses $< 0.03\, M_\odot$; we
also compare with other IMFs in current use.
