Fundamental normality test

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 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:

See also

• Montel's theorem