a theorem that gives an expression in terms of an integral for the value of an analytic function at any point inside a simple closed curve of finite length in a domain.
the theorem that the integral of an analytic function about a closed curve of finite length in a finite, simply connected domain is zero.
- Cauchy-Riemann equations
equations relating the partial derivatives of the real and imaginary parts of an analytic function of a complex variable, as f (z) = u (x,y) + iv (x,y), by δ u /δ x = δ v /δ y and δ u /δ y = −δ v /δ x.
- Cauchy-Schwarz inequality
Schwarz inequality (def 2).