Cauchy-Riemann equation

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English

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Etymology

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Named after mathematicians Augustin Cauchy (1789-1857) and Bernhard Riemann (1826-1866).

Noun

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Cauchy-Riemann equation (plural Cauchy-Riemann equations)

  1. (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations or , which together form part of the criteria that f be complex-differentiable.
  2. (complex analysis) The equivalent single equation .