Cauchy-Riemann equations

[ koh-shee-ree-mahn, koh-shee- ]

plural noun

, Mathematics.

1. equations relating the partial derivatives of the real and imaginary parts of an analytic function of a complex variable, as f ( z ) = u ( x,y ) + iv ( x,y ), by δ u /δ x = δ v /δ y and δ u /δ y = −δ v /δ x.

Word History and Origins

Origin of Cauchy-Riemann equations¹

Named after A. L. Cauchy and G. F. B. Riemann

Example Sentences

Other winners of the equation beauty contest included the Pythagorean identity, the identity between exponential and trigonometric functions derivable from Euler’s formula for complex analysis, and the Cauchy-Riemann equations.

From Scientific American