By Frank Miller, Neil Gaiman et al.
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The phase is φ = ωdt where ω is the orbital frequency, from which one deduces φ = − (ω/L)dE. The result is simpler if we use instead of the local time t flowing in the observer’s frame (t = T − R/c with the notation of Section 3) the adimensional time variable  c3 ν (tc − t) , (66) 5GM where tc denotes the instant of coalescence (at which the frequency goes formally to infinity). In terms of this time variable the orbital phase is obtained as Θ= φ(t) = φ0 − 1 Θ5/8 + ν 3715 55 3π 1/4 + ν Θ3/8 − Θ 8064 96 4 + 284875 1855 2 9275495 + ν+ ν Θ1/8 14450688 258048 2048 − 38645 15 + ν π ln Θ + O(Θ−1/8 ) 172032 2048 , (67) where φ0 is some constant phase determined by initial conditions (for instance when the signal enters the frequency bandwidth of the detector).
197 (1975) 717. , Ann. Phys. ) 11 (1960) 169.  Bonnor W. , Rotenberg M. , Proc. R. Soc. London A 265 (1961) 109.  Bonnor W. , Rotenberg M. , Proc. R. Soc. London A 289 (1966) 247.  Hunter A. , Rotenberg M. , J. Phys. A 2 (1969) 34.  Bonnor W. , Ondes et radiations gravitationnelles (CNRS, Paris, 1974) p. 73.  Thorne K. , Kov´acs S. , Astrophys. J. 200 (1975) 245.  Crowley R. , Thorne K. , Astrophys. J. 215 (1977) 624.  Thorne K. , Rev. Mod. Phys. 52 (1980) 299. , Philos.
For convenience we denote by x = (GM ω/c3 )2/3 a small dimensionless post-Newtonian parameter of order ε2 , where ω is the instantaneous angular frequency of the orbit (ω = 2π/P , where P is the orbital period). 5PN–accurate luminosity L of the binary is obtained by application of the formalism above. Namely, one uses the decomposition of L in terms of observable moments UL and VL as given by (25). Then one relates the observable moments to the moments ML and SL by the equations (36)-(40). 5PN order the mass quadrupole moment comprises the dominant tail integral and the quadrupole-quadrupole interaction terms which include the nonlinear memory integral, but the tail of tail integral appearing in (39) is negligible.
Batman Black and White Vol.2 by Frank Miller, Neil Gaiman et al.