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The description of the electron oscillations of a collisionless plasma by the usual residual presentation is insufficient in the initial phase of time development and for perturbations of small velocity spread. We derived criteria for the number of residual terms which have to be taken into account and obtain analytic expressions for the remaining integral. Decomposing the initial perturbation into velocity beams we show that Landau damping is due to phase mixing caused by free streaming of particle beams modified through the response of the main plasma body.