If a function is analytic within a simple closed loop, the integral around that loop is zero.
Allows you to find the value of an analytic function inside a boundary just by knowing its values on the boundary. It implies that if a function is differentiable once, it is infinitely differentiable. Complex Analysis for Mathematics and Engineerin...
A powerful tool for evaluating complex (and difficult real) integrals by looking at "poles" (singularities) where the function blows up. 3. Series and Singularities If a function is analytic within a simple
Representing functions as infinite sums. Laurent series are particularly useful because they describe functions near their singularities. Complex Analysis for Mathematics and Engineerin...