Cauchy's Inequality (idea)

Cauchy's inequality is named after Augustin Cauchy
Let z₀ be a fixed complex number. If a function f is analytic within and on a circle centered at z₀ with radius R, and the values on C of M_R are strictly <= |f(z)|

f⁽ⁿ⁾(z₀) <= (n!)(M_R)/(r^n)

See also Liouville's Theorem.