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[[복소수,complex_number]] $z=x+iy$ 일 때
[[복소함수,complex_function]] $f(z)=u(x,y)+iv(x,y)$ 가 미분가능 하기 위한?? 가 analytic하기 위한([[해석함수,analytic_function]]?) 필충조건?? 필요조건? CHK

//wpen
"....form a necessary and sufficient condition for a complex function to be holomorphic (complex differentiable)."
[[정칙함수,holomorphic_function]] or [[정칙함수,regular_function]] - 둘 아마 같은듯? - writing


에서 <- 이게뭐지? ....assumption/precondition을 나중에 적으려고 했던건가?
 $u_x=v_y$
 $u_y=-v_x$
or
 $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}$
 $\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x}$
CHK!!!

f가 해석적이면, 실수부 함수 u와 허수부 함수 v는 서로에 대해 공액조화함수/켤레조화함수 conjugate harmonic function CHK

찾다 보면 [[조화함수,harmonic_function]] and [[라플라스_방정식,Laplace_equation]] 언급됨.


Twins:
[[https://terms.naver.com/entry.naver?docId=4125471&ref=y&cid=60207&categoryId=60207 수학백과: 코시-리만 방정식]]
https://mathworld.wolfram.com/Cauchy-RiemannEquations.html
https://everything2.com/title/Cauchy-Riemann+equations
https://en.wikiversity.org/wiki/Cauchy-Riemann_Equations (정리와 증명)
https://encyclopediaofmath.org/wiki/Cauchy-Riemann_equations
[[WpEn:Cauchy–Riemann_equations]]
[[WpKo:코시-리만_방정식]]

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Up: 연립 [[편미분방정식,partial_differential_equation,PDE]]