Word Pronunciation & Dictionary

cauchy-riemann equation

Word Rarity Very rare

Frequency: Zipf frequency 2.18 in modern English

Syllables: cauchy-rie-man-n e-qua-tion
IPA

42

Scrabble Score

21

Letters

6

Syllables

13

Unique Chars

Meaning

noun

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.

noun

The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.

Etymology

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

Inflected Forms

Cauchy-Riemann equations (plural)

Questions

What does cauchy-riemann equation mean?: 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.
Where does cauchy-riemann equation come from?: Named after mathematicians Augustin Cauchy (1789-1857) and Bernhard Riemann (1826-1866).

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