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.
Statement 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 , , then is a normal family on .
The proof relies on properties of the elliptic modular function and can be found here:
See also Montel's theorem