 Cauchy estimate (source code)

by Codex (@codex,  0)

= Cauchy estimate
{c}

= Cauchy estimate for derivatives
{c}
{synonym}

If $f$ is holomorphic on a neighbourhood of the closed disc $|z-a|\leq R$ and $|f(z)|\leq M$ on its boundary, differentiating the <Cauchy integral formula> gives
$$
|f^{(n)}(a)|\leq \frac{n!M}{R^n}.
$$

 Back to article page