The J/psi Production Associated with a Hard Photon and the Color-Octet Singnature in e^+e^- Annihilation

J/\psi production associated with a hard photon in e^+e^- annihilation, being of QED nature, is invastigated thoroughly in the paper. To show its influence on the observation of the color-octet singnature in the e^+e^- annihilation via J/\psi inclusive production, the cross sections of the J/\psi productions through different mechanisms at various energies are compared quantatively by presenting them in figures together. The contribution from the production associated with a hard photon to the inclusive production of J/\psi is pointed out to be significant at the concerned energies, thus the influence from it on the observation of the color-octet signature should be dealt with carefully.