"complex-differentiable" meaning in English

See complex-differentiable in All languages combined, or Wiktionary

Adjective

Head templates: {{en-adj|-}} complex-differentiable (not comparable)
  1. (mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane. Tags: not-comparable Categories (topical): Complex analysis, Mathematics Synonyms: complex differentiable Synonyms (differentiable and that satisfies the Cauchy-Riemann Equations on a subset of the complex plane): analytic, holomorphic Synonyms (differentiable and that satisfies the Cauchy-Riemann Equations on the complex plane): entire, integral
    Sense id: en-complex-differentiable-en-adj-OXqfUANs Categories (other): English entries with incorrect language header, Pages with 1 entry Topics: complex-analysis, mathematics, sciences
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          "ref": "1993, Victor Khatskevich, David Shoiykhet, Differentiable Operators and Nonlinear Equations, page 75",
          "text": "This gives the possibility to extend the well-established theory of complex-differentiable operators, a theory with meany deep results.",
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          "ref": "2010, Luis Manuel Braga da Costa Campos, Complex Analysis with Applications to Flows and Fields, page 335",
          "text": "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).",
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          "ref": "2010, Peter J. Schreier, Louis L. Scharf, Statistical Signal Processing of Complex-Valued Data, Cambridge University Press, page 277",
          "text": "We can of course regard a function f defined on #x5C;mathbb#x7B;R#x7D;#x7B;2n#x7D; as a function defined on #x5C;mathbb#x7B;C#x7D;#x7B;n#x7D;. If f is differentiable on #x5C;mathbb#x7B;R#x7D;#x7B;2n#x7D;, it is said to be real-differentiable, and if f is differentiable on #x5C;mathbb#x7B;C#x7D;#x7B;n#x7D;, it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.",
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        "(mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane."
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