Question

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

score 58 · Answer 1 · 2026-03-25 03:24:13

58

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

Published on 25 Mar 2026 - 3:24

score 1.9k · Answer 2 · 2026-03-25 03:19:45

1.9k

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

Published on 25 Mar 2026 - 3:19

score 239 · Answer 3 · 2026-03-22 08:05:26

239

Views

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

Published on 22 Mar 2026 - 8:05

score 255 · Answer 4 · 2026-03-22 06:01:54

255

Views

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

Published on 22 Mar 2026 - 6:01

score 165 · Answer 5 · 2026-03-21 21:31:53

165

Views

Prove that Cauchy-Riemann Equations are satisfied.

Published on 21 Mar 2026 - 21:31

score 3.5k · Answer 6 · 2026-03-22 00:26:11

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 22 Mar 2026 - 0:26

score 80 · Answer 7 · 2026-03-22 14:50:12

80

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Cauchy Riemann equations for a Riemann sphere?

Published on 22 Mar 2026 - 14:50

score 10k · Answer 8 · 2026-03-21 18:51:57

10k

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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 21 Mar 2026 - 18:51

score 468 · Answer 9 · 2026-03-25 04:58:46

468

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 25 Mar 2026 - 4:58

score 105 · Answer 10 · 2026-03-22 02:28:36

105

Views

Partial derivative proof of complex numbers

Published on 22 Mar 2026 - 2:28

score 95 · Answer 11 · 2026-03-22 05:59:48

95

Views

Cauchy-Riemann equations for square root

Published on 22 Mar 2026 - 5:59

score 111 · Answer 12 · 2026-03-21 22:30:45

111

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

Published on 21 Mar 2026 - 22:30

score 152 · Answer 13 · 2026-03-21 21:40:16

152

Views

Using Taylor's theorem to prove Cauchy Riemann equations

Published on 21 Mar 2026 - 21:40

score 1.8k · Answer 14 · 2026-03-22 01:04:53

1.8k

Views

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

Published on 22 Mar 2026 - 1:04

score 1.3k · Answer 15 · 2026-03-25 06:30:23

1.3k

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

Published on 25 Mar 2026 - 6:30

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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