First, we rewrite the summation in (3) as a difference of fractional harmonic numbers: 2 Using the recurrence for harmonic numbers: We then use the asymptotic expansion, H F ≈ log F + γ + 1 2F , omiting trailing terms which are O(F −2 ) and smaller powers of F : 3 Omitting the trailing term leads to the approximation in Antoniak (1974).
due to a misinterpretation of Antoniak (1974), GGJ06 use an approximation that leaves out all the P 1 (w) terms from (4).