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In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions.
Statement of theorem
Let be a family of analytic functions defined on a domain . If there are two fixed complex numbers a and b that are omitted from the range of every ƒ ∈ , then is a normal family on .
The proof relies on properties of the elliptic modular function and can be found here:
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