ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Partially ordered map
Ordered map
Path
Real path
Euclidean real path
Complex path
Continuously differentiable complex path
Definition D5648
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}
Children
Complex oriented curve integral