Residue Theorem: Let $\text{[math]}$ be analytic in the region $\text{[math]}$ except for the isolated singularities $\text{[math]}$ . If $\text{[math]}$ is a closed rectifiable curve in $\text{[math]}$ which does not pass through any of the points $\text{[math]}$ and if $\text{[math]}$ in $\text{[math]}$ , then

$\text{[math]}$

Maximum Modulus: Let $\text{[math]}$ be a bounded open set in $\text{[math]}$ and suppose that $\text{[math]}$ is a continuous function on $\text{[math]}$ which is analytic in $\text{[math]}$ . Then

$\text{[math]}$

First some large operators both in text: $\text{[math]}$ and $\text{[math]}$ ; and also on display:

$\text{[math]}$

And some plot from here:

$\text{[math]}$

Finally, some algorithm from here!

$\text{[math]}$