The numerical solution of partial differential equations requires suitable boundary conditions. Based on a fundamental integral relation for Legendre polynomials, Marshak type boundary conditions are derived that can be applied if an expansion in Legendre polynomials is utilized to solve the spatially inhomogeneous kinetic equation of the electrons in gas discharge plasmas. In particular, it is now possible to relate directly the expansion coefficients of the phase space distribution with macroscopic quantities at the boundaries. That is, a well-defined influx or a reflection of electrons can easily be treated on the microscopic level.