Abstract
Let {f n } be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {h n } be a sequence of meromorphic functions on D, whose poles are multiple, such that {h n } converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D. If f′ n ≠ h n , then {f n } is normal on D.
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Chen, Q., Yang, L. & Pang, X. Normal family and the sequence of omitted functions. Sci. China Math. 56, 1821–1830 (2013). https://doi.org/10.1007/s11425-013-4580-6
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DOI: https://doi.org/10.1007/s11425-013-4580-6