mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form...
33 KB (4,941 words) - 07:41, 23 January 2024
the Cauchy–Riemann equations in the region bounded by γ {\displaystyle \gamma } , and moreover in the open neighborhood U of this region. Cauchy provided...
10 KB (1,635 words) - 21:31, 20 December 2022
continuous first derivatives which solve the Cauchy–Riemann equations, a set of two partial differential equations. Every holomorphic function can be separated...
23 KB (2,820 words) - 06:03, 13 April 2024
solve the inhomogeneous Cauchy–Riemann equations in D. Indeed, if φ is a function in D, then a particular solution f of the equation is a holomorphic function...
25 KB (4,361 words) - 17:59, 16 June 2024
f(z) be analytic is that u and v be differentiable and that the Cauchy–Riemann equations be satisfied: u x = v y , v x = − u y . {\displaystyle u_{x}=v_{y}...
32 KB (4,943 words) - 16:26, 10 June 2024
curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation. Introduced in 1985 by Mikhail...
7 KB (1,045 words) - 10:50, 21 February 2022
differential equations has the following properties. If u {\displaystyle u} and v {\displaystyle v} are solutions of the Cauchy–Riemann equations, then u {\displaystyle...
6 KB (916 words) - 13:02, 23 July 2022
}}=-{\frac {\partial \Phi }{\partial \rho }}} The Cauchy–Riemann equations can also be written in one single equation as ( ∂ ∂ x + i ∂ ∂ y ) f ( x + i y ) = 0...
10 KB (1,661 words) - 00:47, 18 June 2024
Residue theorem (redirect from Cauchy residue theorem)
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...
13 KB (3,251 words) - 13:48, 29 March 2024
This is a list of equations, by Wikipedia page under appropriate bands of their field. The following equations are named after researchers who discovered...
5 KB (103 words) - 14:59, 5 February 2024