Cauchy's

inequality is named after

Augustin Cauchy
Let z

_{0} be a fixed

complex number. If a

function f is

analytic within and on a

circle centered at z

_{0} with

radius R, and the values on C of M

_{R} are strictly <=
|f(z)|

f^{(n)}(z_{0}) <= (n!)(M_{R})/(r^n)

See also Liouville's Theorem.