Reexamination for the calculation of elliptic flow and other fourier harmonics

We have argued that the azimuthal symmetry and asymmetry components in fourier expansion of particle momentum azimuthal distribution, $v_n$ (n=0, 1, 2, …), should be calculated as an average of $cos(n\varphi )$ first over particles in an event and then over events (event-wise average) rather than “an average over all particles in all events” (particle-wise average). In case of large centrality (multiplicity) bin the particle-wise average is not accurate because the influence (fluctuation) of particle multiplicity was not taken into account.