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.

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 ∈

The proof relies on properties of the elliptic modular function and can be found here: J. L. Schiff (1993).