Complex-differentiable

Quick meaning: Complex-differentiable is an adjective meaning (mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.

Meaning

(mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.

Example Sentences

This gives the possibility to extend the well-established theory of complex-differentiable operators, a theory with meany^([sic]) deep results.

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).

We can of course regard a function f defined on #92;mathbb#123;R#125;#123;2n#125; as a function defined on #92;mathbb#123;C#125;#123;n#125;. If f is differentiable on #92;mathbb#123;R#125;#123;2n#125;, it is said to be real-differentiable, and if f is differentiable on #92;mathbb#123;C#125;#123;n#125;, it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.

Synonyms for complex-differentiable

Depending on context, synonyms include analytic, holomorphic, entire, integral.

Related Words

Related dictionary entries include entire, holomorphic, differentiable, complex, quasi-differentiable, quasidifferentiable.

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