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complex-differentiable

別の表記

complex differentiable

形容詞

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 f {\displaystyle f} $f$ defined on R 2 n {\displaystyle \mathbb {R} ^{2n}} $\mathbb {R} ^{2n}$ as a function defined on C n {\displaystyle \mathbb {C} ^{n}} $\mathbb {C} ^{n}$ . If f {\displaystyle f} $f$ is differentiable on R 2 n {\displaystyle \mathbb {R} ^{2n}} $\mathbb {R} ^{2n}$ , it is said to be real-differentiable, and if f {\displaystyle f} $f$ is differentiable on C n {\displaystyle \mathbb {C} ^{n}} $\mathbb {C} ^{n}$ , it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.

使用する際の注意点

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

同意語

(differentiable かつ that satisfies the Cauchy-Riemann Equations on a subset of the complex plane): analytic, holomorphic
(differentiable かつ that satisfies the Cauchy-Riemann Equations on the complex plane): entire, integral

参考

Cauchy-Riemann Equations on Wikipedia.

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