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Continuously differentiable complex path integral
Formulation 0
Let $\gamma : [a, b] \to \mathbb{C}$ be a D5647: Continuously differentiable complex path such that
(i) $f : \gamma([a, b]) \to \mathbb{C}$ is a D5635: Standard-continuous complex function
The complex path integral of $f$ with respect to $\gamma$ is the D1207: Complex number \begin{equation} \int_{\gamma} f(z) \, d z : = \int^b_a f(\gamma(t)) \gamma'(t) \, d t \end{equation}
Child definitions
» D5649: Complex oriented curve integral