Definition:Cauchy Integral
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Definition
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:
- $\ds A = \lim_{\delta x \mathop \to 0} \sum \map f x \rdelta x$
Also see
- Results about Cauchy integrals can be found here.
Source of Name
This entry was named for Augustin Louis Cauchy.
Historical Note
The method of forming a definite integral known as a Cauchy integral was first put forward by Augustin Louis Cauchy.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cauchy integral
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integration
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cauchy integral
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integration