[en] Approximation methods based on the systematic expansions of the modulating function are presented for potential scattering. It is shown that three types of the systematic methods, which are related to the eikonal type approximations, can be developed. These three expansions are expected to give the excellent approximations for the respective ranges of forward, backward and intermediate scattering angles at high energies. The functional integral representations for various propagators are given in closed form on the basis of the method proposed by Fradkin. The relations among systematic expansions and an approximation method for the functional integral are illustrated. (auth.)