See complex-differentiable on Wiktionary
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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^([sic]) 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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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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