If a transcendental meromorphic function f with finitely many poles has a completely invariant domain U which is simply connected and satisfies some conditions, we prove F(f) = U. And for a transcendental meromorphic function f with the lower order mu infinity and delta (infinity, f) 0, we prove J (f) cannot be contained in any finite set of straight lines completely. (C) 2007 Elsevier Inc. All rights reserved.
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