Liu Ke-xiao
Abstract
Let ￡ be a family of meromorphic functions on the plain domain D,a1,a2 and a3 are three distinct complex numbers.If for every f∈F,f∈S={a1,a2,a3}f(k)∈S,and the zeros of f-a1(a1≠0,otherwise a2 or a3)are of multiplicity at least k+1,then ￡ is normal on D.
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Let ￡ be a family of meromorphic functions on the plain domain D,a1,a2 and a3 are three distinct complex numbers.If for every f∈F,f∈S={a1,a2,a3}f(k)∈S,and the zeros of f-a1(a1≠0,otherwise a2 or a3)are of multiplicity at least k+1,then ￡ is normal on D.
Key concepts: Meromorphic function, Normality, Multiplicity (mathematics), Normal family, Mathematics, Pure mathematics, Domain (mathematical analysis), Combinatorics