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The formalisms of helicity coupling amplitudes for J/ψ→π+π-π0 are presented. A detailed discussion is also given on the barrier factor, Breit-Wigner, and density matrix. A Monte Carlo simulation of J/ψ→ρ(770)π→π+π-π0 is carried out. The results show that the ρ(770) resonance is well reproduced compared with experimental data.