In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions. It is another name for the stronger version of Montel's theorem.
Let be a family of analytic functions defined on a domain . If there are two fixed complex numbers a and b such that for all ƒ ∈ and all x ∊ , f(x) ∉ {a, b}, then is a normal family on .
The proof relies on properties of the elliptic modular function and can be found here: J. L. Schiff (1993). Normal Families. Springer-Verlag. ISBN 0-387-97967-0.
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