THE GROWTH OF COMPOSITE MEROMORPHIC FUNCTIONS WITH DEFICIENT FUNCTIONS

Jianwu Sun

Abstract

          Let f be a transcendental meromorphic function of order ρ_f , g a transcendental entire function of lower order λ_g (λ_g<+∞ ), and a_i(z) (i=1, 2, ..., n; n ≤ ∞) be entire funtions satifying T(r, a_i(z)) = o(T(r,g)).

If

n ∑ i = 1

δ(ai(z),g)=1, δ(ai(z),g)>0 and ai(z) \not\equiv ∞ for each i, then

____   lim   r → ∞

log(T(r, f(g))) / T(r, g) = πρf .