On deviations and strong asymptotic functions of meromorphic functions of finite lower order

Let f   be a transcendental meromorphic function of finite lower order with N(r,f)=S(r,f)N(r,f)=S(r,f), and let qνqν be distinct rational functions, 1⩽ν⩽k1⩽ν⩽k. For 0<γ<∞0<γ<∞ putB(γ):={πγsinπγif γ⩽0.5,πγif γ>0.5. The estimate of the lower and upper logarithmic density of the setE(γ)={r:∑1⩽ν⩽klog+max|z|=r|f(z)−qν(z)|−1