complex-differentiable
Adjective
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Adjective
complex-differentiable (not comparable)
- (mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.
- 1993, Victor Khatskevich, David Shoiykhet, Differentiable Operators and Nonlinear Equations, page 75 ↗,
- This gives the possibility to extend the well-established theory of complex-differentiable operators, a theory with meany
[ sic] deep results.
- This gives the possibility to extend the well-established theory of complex-differentiable operators, a theory with meany
- 2010, Luis Manuel Braga da Costa Campos, Complex Analysis with Applications to Flows and Fields, page 335 ↗,
- Further it can be shown that the holomorphic function also has a convergent Taylor series, that is, a complex differentiable function is also an analytic function (Section 23.7).
- 2010, Peter J. Schreier, Louis L. Scharf, Statistical Signal Processing of Complex-Valued Data, Cambridge University Press, page 277 ↗,
- We can of course regard a function f defined on \mathbb{R}^{2n} as a function defined on \mathbb{C}^{n}. If f is differentiable on \mathbb{R}^{2n}, it is said to be real-differentiable, and if f is differentiable on \mathbb{C}^{n}, it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.
- 1993, Victor Khatskevich, David Shoiykhet, Differentiable Operators and Nonlinear Equations, page 75 ↗,
- (differentiable and that satisfies the Cauchy-Riemann Equations on a subset of the complex plane) analytic, holomorphic
- (differentiable and that satisfies the Cauchy-Riemann Equations on the complex plane) entire, integral
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004