Meromorphic function of infinite order with maximum deficiency sum

Abstract

In this paper we prove the following theorem: Let f(z) be a meromorphic function of infinite order. If Σ_a≠∞δ(a, f)+δ(∞, f)=2, then for each positive integer k, we have K(f^(k))=2k(1−δ(∞, f))/(1+k−kδ(∞, f)), where K(f^(k))=lim_r→∞(N(r, 1/f^(k))+N(r, f^(k)))/T(r, f^(k)) exists. This result improves the results by S. K. Singh and V. N. Kulkarni [1] and Mingliang Fang [2].