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Theoretical investigations of DC discharge plasmas in reactors with plane electrodes are presented. A multiterm method for the solution of the space-dependent Boltzmann equation of the electrons has been adopted and modified to analyze the behavior of the velocity distribution function and of relevant macroscopic properties of the electron component in oxygen discharge plasmas for a wide range of pressure and applied voltage. On the basis of the results, the main features of the kinetics of the electrons are discussed. In particular, the analysis shows drastic changes of the properties of the electron gas in the transition from the regime with almost negligible impact of collisions at lower pressure to the collision-dominated plasma at higher pressure. Regarding the multiterm method, it is found that the convergent solution of the Boltzmann equation of the electrons is generally obtained, where the conventionally used two-term approximation still gives fair results at lower applied voltages and pressures around 100 Pa, but a multiterm method with up to ten terms is required when decreasing the pressure by almost one order of magnitude.