English Explanatory Dictionary

Cauchy-Riemann equation

English dictionary entry

Meanings

noun
  1. 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 (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
  2. The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.

Word forms

Cauchy-Riemann equation Cauchy-Riemann equations

Etymology

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

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