Category:Definitions/Cauchy Integrals

This category contains definitions related to Cauchy Integrals.
Related results can be found in Category:Cauchy Integrals.

Let $f$ be a continuous real function.

Let $\closedint a b$ be a closed real interval such that $a < b$.

Let $P = \set {a, x_1, x_2, \ldots, x_{n - 1}, b}$ be a normal subdivision of $\closedint a b$ such that $x_k - x_{k - 1} = \delta x$.

The Cauchy integral of $f$ from $a$ to $b$ is defined as:

$\ds A = \lim_{\delta x \mathop \to 0} \sum \map f x \rdelta x$