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 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,
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