Definition:Cauchy Principal Value/Complex Integral

Definition
Let $f: \R \to \C$ be a bounded complex function.

Then the Cauchy principal value of $\ds \int f$ is defined as:


 * $\PV_{-\infty}^{+\infty} \map f t \rd t := \lim_{R \mathop \to +\infty} \int_{-R}^R \map f t \rd t$

where $\ds \int_{-R}^R \map f t \rd t$ is a complex Riemann integral.