[en] To overcome difficulties with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions at positive energies are considered. It is shown that resonance functions (the Gamow functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials is obtained and discussed. To illustrate general proofs of convergence of the obtained expansions some examples of delta potentials and square well are considered. Numerical calculations show the convergence of these expansions to be fast