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We derive a semi-empirical galactic initial mass function (IMF) fromobservational constraints. We assume that the star formation rate in a galaxycan be expressed as the product of the IMF, $\psi (m)$, which is a smoothfunction of mass $m$ (in units of \msun), and a time- and space-dependent totalrate of star formation per unit area of galactic disk. The mass dependence ofthe proposed IMF is determined by five parameters: the low-mass slope $\gamma$,the high-mass slope $-\Gamma$, the characteristic mass $m_{ch}$ (which is closeto the mass $m_{\rm peak}$ at which the IMF turns over), and the lower andupper limits on the mass, $m_l$ (taken to be 0.004) and $m_u$ (taken to be120). The star formation rate in terms of number of stars per unit area ofgalactic 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 stellarmasses. The values of $\gamma$ and $\emch$ are derived from two integralconstraints: 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 massdistribution of field stars in the local neighborhood, and ii) the ratio of thenumber of stars in the range $m=0.08 - 1$ to the number of brown dwarfs in therange $m=0.03-0.08$ in young clusters. The IMF satisfying the above constraintsis characterized by the parameters $\gamma=0.51$ and $\emch=0.35$ (whichcorresponds to $m_{\rm peak}=0.27$). This IMF agrees quite well with theChabrier (2005) IMF for the entire mass range over which we have compared withdata, but predicts significantly more stars with masses $< 0.03\, M_\odot$; wealso compare with other IMFs in current use.

An Initial Mass Function for Individual Stars in Galactic Disks: I. Constraining the Shape of the IMF