Question

Is $f(z)=k\cdot\frac{e^z}{z}$ analytic?

score 60 · Answer 1 · 2026-04-28 21:45:13

60

Views

Is $f(z)=k\cdot\frac{e^z}{z}$ analytic?

Published on 28 Apr 2026 - 21:45

score 1.9k · Answer 2 · 2026-04-28 18:21:53

1.9k

Views

If $u(x,y)$ is not a harmonic function, can a harmonic conjugate $v(x,y)$ be found?

Published on 28 Apr 2026 - 18:21

score 242 · Answer 3 · 2026-04-28 18:22:13

242

Views

$f$ is $\mathbb{R}$ - differentiable iff $Re(f)$ and $Im(f)$ are $\mathbb{R}$ - differentiable

Published on 28 Apr 2026 - 18:22

score 258 · Answer 4 · 2026-04-28 18:20:16

258

Views

Complex function only differentiable in $y=x^2$

Published on 28 Apr 2026 - 18:20

score 168 · Answer 5 · 2026-04-28 18:24:04

168

Views

Prove that Cauchy-Riemann Equations are satisfied.

Published on 28 Apr 2026 - 18:24

score 3.5k · Answer 6 · 2026-04-28 18:56:09

3.5k

Views

Using the Cauchy-Riemann Equations, prove that $\operatorname{Log}(z)$ is holomorphic in $\mathbb{C}\setminus[0,\infty)$ and explain why

Published on 28 Apr 2026 - 18:56

score 83 · Answer 7 · 2026-04-28 18:26:00

83

Views

Cauchy Riemann equations for a Riemann sphere?

Published on 28 Apr 2026 - 18:26

score 10k · Answer 8 · 2026-04-28 18:21:55

10k

Views

Show that the function $u(x,y) =e^{x^2−y^2}\cos(2xy )$is harmonic. Find the harmonic conjugate v of u, up to addition of a constant.

Published on 28 Apr 2026 - 18:21

score 470 · Answer 9 · 2026-04-28 18:23:58

470

Views

How do I show that $w = \frac{1}{(z-a)^n}$ is an analytic function using the Cauchy Riemann equations,where z = x + iy?

Published on 28 Apr 2026 - 18:23

score 107 · Answer 10 · 2026-04-28 18:19:32

107

Views

Partial derivative proof of complex numbers

Published on 28 Apr 2026 - 18:19

score 98 · Answer 11 · 2026-04-28 18:20:17

98

Views

Cauchy-Riemann equations for square root

Published on 28 Apr 2026 - 18:20

score 113 · Answer 12 · 2026-04-28 18:19:30

113

Views

Does this formula derived from the Cauchy-Riemann differential equations have a name?

Published on 28 Apr 2026 - 18:19

score 155 · Answer 13 · 2026-04-28 18:23:58

155

Views

Using Taylor's theorem to prove Cauchy Riemann equations

Published on 28 Apr 2026 - 18:23

score 1.8k · Answer 14 · 2026-04-28 18:23:59

1.8k

Views

How to deduce the analyticity of a function, $f(z) = \sin (2z)$

Published on 28 Apr 2026 - 18:23

score 1.3k · Answer 15 · 2026-04-28 18:28:10

1.3k

Views

Show that if $f$ is analytic then $g(z)=\overline{f(\overline{z})}$ is analytic and find its derivative

Published on 28 Apr 2026 - 18:28

List Question

Is $f(z)=k\cdot\frac{e^z}{z}$ analytic?

If $u(x,y)$ is not a harmonic function, can a harmonic conjugate $v(x,y)$ be found?

$f$ is $\mathbb{R}$ - differentiable iff $Re(f)$ and $Im(f)$ are $\mathbb{R}$ - differentiable

Complex function only differentiable in $y=x^2$

Prove that Cauchy-Riemann Equations are satisfied.

Using the Cauchy-Riemann Equations, prove that $\operatorname{Log}(z)$ is holomorphic in $\mathbb{C}\setminus[0,\infty)$ and explain why

Cauchy Riemann equations for a Riemann sphere?

Show that the function $u(x,y) =e^{x^2−y^2}\cos(2xy )$is harmonic. Find the harmonic conjugate v of u, up to addition of a constant.

How do I show that $w = \frac{1}{(z-a)^n}$ is an analytic function using the Cauchy Riemann equations,where z = x + iy?

Partial derivative proof of complex numbers

Cauchy-Riemann equations for square root

Does this formula derived from the Cauchy-Riemann differential equations have a name?

Using Taylor's theorem to prove Cauchy Riemann equations

How to deduce the analyticity of a function, $f(z) = \sin (2z)$

Show that if $f$ is analytic then $g(z)=\overline{f(\overline{z})}$ is analytic and find its derivative

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