Based on the ingoing wave functions discussed in Section 3 and 4, we can derive the gravitational wave energy and angular momentum flux emitted to infinity. The formula for the energy and the angular momentum luminosity to infinity are given by Equations (48) and (49). Since most of the calculations are very long, we show only the final results. In , some details of the calculations are summarized. We define the post-Newtonian expansion parameter by , where is the mass of the black hole and is the orbital angular frequency of the particle. Since the parameter is directly related to the observable frequency, this result can be compared with the results by another method easily.
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