# complex-differentiable

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## English

[edit]### Alternative forms

[edit]### Adjective

[edit]**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.

**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 defined on as a function defined on . If is differentiable on , it is said to be real-differentiable, and if is differentiable on , it is
. A function is**complex-differentiable****complex-differentiable**if and only if it is real-differentiable and the Cauchy-Riemann equations hold.

#### Usage notes

[edit]The form *complex differentiable* appears to be more common, although the construction is perhaps ambiguous.

#### Synonyms

[edit]- (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

### See also

[edit]-
**Cauchy-Riemann Equations**on Wikipedia.Wikipedia