complex-differentiable

alternative complex differentiable

1. not comparablecomplex analysisThat is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.

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

   1993, Victor Khatskevich, David Shoiykhet, Differentiable Operators and Nonlinear Equations, page 75

   2 more examples

   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, Luis Manuel Braga da Costa Campos, Complex Analysis with Applications to Flows and Fields, page 335

   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.

   2010, Peter J. Schreier, Louis L. Scharf, Statistical Signal Processing of Complex-Valued Data, Cambridge University Press, page 277

   Synonyms: analytic, holomorphic, entire, integral