Question

Why does an analytic function $z^2$, which satisfies the Cauchy-Riemann equations, not satisfy the condition of being harmonic?

score 72 · Answer 1 · 2020-11-15 21:18:20

72

Views

Why does an analytic function $z^2$, which satisfies the Cauchy-Riemann equations, not satisfy the condition of being harmonic?

Published on 15 Nov 2020 - 21:18

score 177 · Answer 2 · 2020-11-18 00:40:02

177

Views

Does this piecewise function satisfy the Cauchy Riemann equations?

Published on 18 Nov 2020 - 0:40

score 547 · Answer 3 · 2020-11-28 17:51:14

547

Views

Let $f(z) = u(x,y) + iv(x,y)$ be an holomorphic function and $2u(x,y) + v(x,y) = 5$. Show that $f$ is constant

Published on 28 Nov 2020 - 17:51

score 32 · Answer 4 · 2020-11-29 21:38:12

32

Views

How can I take a partial derivative of an equation like $2u+v=5$?

Published on 29 Nov 2020 - 21:38

score 385 · Answer 5 · 2020-12-08 15:12:29

385

Views

Question regarding analyticity, differentiability and the Cauchy-Riemann Equations ( Complex Analysis )

Published on 08 Dec 2020 - 15:12

score 64 · Answer 6 · 2020-12-10 13:56:17

64

Views

Prove $\int_1^{\infty}\psi(x)(x^\frac{s}{2}+ x^\frac{1-s}{2})\frac{dx}{x} $ is Entire

Published on 10 Dec 2020 - 13:56

score 127 · Answer 7 · 2020-12-11 22:09:27

127

Views

Show that the inverse function also satisfies C-R equation.

Published on 11 Dec 2020 - 22:09

score 117 · Answer 8 · 2021-01-04 07:41:27

117

Views

Cauchy-Riemann Equations

Published on 04 Jan 2021 - 7:41

score 108 · Answer 9 · 2021-01-08 15:59:19

108

Views

Cauchy-Riemann conditions implied by harmonicity and orthogonal gradients?

Published on 08 Jan 2021 - 15:59

score 42 · Answer 10 · 2021-01-12 19:39:04

42

Views

Find a real-valued function which satisfied Cauchy-Riemann equations

Published on 12 Jan 2021 - 19:39

score 138 · Answer 11 · 2021-01-14 14:49:29

138

Views

show $f$ complex analytic is constant

Published on 14 Jan 2021 - 14:49

score 64 · Answer 12 · 2021-01-16 17:46:05

64

Views

For which $z \in \mathbb{C}$ does $f(z) = |z|^2 +2z$ satisfy Cauchy-Riemann equations?

Published on 16 Jan 2021 - 17:46

score 38 · Answer 13 · 2026-03-25 19:03:11

38

Views

Why $\dfrac{\partial v}{\partial y}=0$ which also gives us $\dfrac{\partial v}{\partial x}=0$?

Published on 25 Mar 2026 - 19:03

score 34 · Answer 14 · 2021-01-27 14:41:04

34

Views

Complex differentiation, Cauchy Riemann

Published on 27 Jan 2021 - 14:41

score 829 · Answer 15 · 2021-01-29 03:27:58

829

Views

Showing the Polar form of the Cauchy-Riemann Equations imply the Cartesian Form

Published on 29 Jan 2021 - 3:27

List Question

Why does an analytic function $z^2$, which satisfies the Cauchy-Riemann equations, not satisfy the condition of being harmonic?

Does this piecewise function satisfy the Cauchy Riemann equations?

Let $f(z) = u(x,y) + iv(x,y)$ be an holomorphic function and $2u(x,y) + v(x,y) = 5$. Show that $f$ is constant

How can I take a partial derivative of an equation like $2u+v=5$?

Question regarding analyticity, differentiability and the Cauchy-Riemann Equations ( Complex Analysis )

Prove $\int_1^{\infty}\psi(x)(x^\frac{s}{2}+ x^\frac{1-s}{2})\frac{dx}{x} $ is Entire

Show that the inverse function also satisfies C-R equation.

Cauchy-Riemann Equations

Cauchy-Riemann conditions implied by harmonicity and orthogonal gradients?

Find a real-valued function which satisfied Cauchy-Riemann equations

show $f$ complex analytic is constant

For which $z \in \mathbb{C}$ does $f(z) = |z|^2 +2z$ satisfy Cauchy-Riemann equations?

Why $\dfrac{\partial v}{\partial y}=0$ which also gives us $\dfrac{\partial v}{\partial x}=0$?

Complex differentiation, Cauchy Riemann

Showing the Polar form of the Cauchy-Riemann Equations imply the Cartesian Form

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