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 $ℱ$ be a family of analytic functions defined on a domain $\mathrm{\Omega }$. If there are two fixed complex numbers a and b such that for all ƒ ∈ $ℱ$ and all $x\in \mathrm{\Omega }$, $f(x)\in ̸\{a,b\}$, then $ℱ$ is a normal family on $\mathrm{\Omega }$.

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

See also

• Montel's theorem