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 $$\mathcal{F} $$ be a family of analytic functions defined on a domain $$ \Omega $$. If there are two fixed complex numbers a and b such that for all &fnof; &isin; $$\mathcal{F}$$ and all x ∊ $$ \Omega $$, f(x) ∉ {a, b}, then $$ \mathcal{F} $$ is a normal family on $$ \Omega $$.

The proof relies on properties of the elliptic modular function and can be found here: