On the logarithmic derivative of a meromorphic function

We derive the following estimate for the quantity m(r,f′/tf) of the Nevanlinna theory of the distribution of values characterizing the growth of the logarithmic derivative of a meromorphic functionf(z),f(0) = 1, 0 < r < R < ∞: m(r,f′/f) < 1n+ [T(R,f)/r (R/R−r)2] + 6.0084. This estimate is more accurate than that obtained earlier by Vu Ngoyan and I. V. Ostrovskii.