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.

See all of Cauchy's Inequality, no other writeups in this node.

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)|

Let z

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

See also Liouville's Theorem.