The Gaussian solution of the transport equation for electrons in a medium omits the large angle single scattering events. These events have been included by using Monte Carlo calculated radial dose profiles for point monodirectional beams. A sum of three Gaussian functions with different relative weights and widths have been fitted to the Monte Carlo calculated radial dose profiles. These profiles have been confirmed by measurements in an almost point monodirectional beam, and the importance of an adequate experimental set-up for determination of radial dose profiles is discussed. The analytic treatment when using three different functions in the Gaussian formalism is presented. Central axis depth dose curves for 10 MeV and 20 MeV have finally been calculated and compared with depth dose curves calculated using Monte Carlo technique and a single Gaussian function. Considerable errors (20-30%) result with the single Gaussian function at small field sizes whereas three components give good agreement with the Monte Carlo method.