Question

Prove or disprove there is an analytic function $F$ on $\{ 1 < |z| < 2\}$ with $\Re F(x+iy) = \log (x^2+y^2)$

score 67 · Answer 1 · 2026-04-17 03:43:24

67

Views

Prove or disprove there is an analytic function $F$ on $\{ 1 < |z| < 2\}$ with $\Re F(x+iy) = \log (x^2+y^2)$

Published on 17 Apr 2026 - 3:43

score 655 · Answer 2 · 2026-04-14 07:56:11

655

Views

Using Cauchy Riemann complex form to prove Cauchy Riemann polar coordinates form

Published on 14 Apr 2026 - 7:56

score 3.6k · Answer 3 · 2026-04-16 00:07:39

3.6k

Views

Domain of analyticity of $f(z) = \frac{1}{z^2}$

Published on 16 Apr 2026 - 0:07

score 114 · Answer 4 · 2026-04-17 04:35:25

114

Views

Proving that if $f=0$ on an arc or region in $D$, where $f$ is analytic on $D$, than $f = 0$ on $D$.

Published on 17 Apr 2026 - 4:35

score 60 · Answer 5 · 2026-05-11 00:31:18

60

Views

Extending uniform convergence of analytic functions on larger domains

Published on 11 May 2026 - 0:31

score 84 · Answer 6 · 2026-04-12 01:52:08

84

Views

Express a complex analytic function as a single power series

Published on 12 Apr 2026 - 1:52

score 1.8k · Answer 7 · 2026-04-16 09:09:10

1.8k

Views

Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.

Published on 16 Apr 2026 - 9:09

score 59 · Answer 8 · 2026-05-07 01:26:07

59

Views

For $|q|<1$, the function $\frac{(az;q)_\infty}{(z;q)_\infty}$ is analytic on $|z|<1$.

Published on 07 May 2026 - 1:26

score 60 · Answer 9 · 2026-05-10 17:20:20

60

Views

Properties of Complex Function $f(z)=e^{-\frac{1}{z^{1/3}}}$

Published on 10 May 2026 - 17:20

score 545 · Answer 10 · 2026-04-17 04:41:07

Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `

score 71 · Answer 11 · 2026-04-16 21:12:04

71

Views

Show that a function is analytic on the punctured complex plane

Published on 16 Apr 2026 - 21:12

score 49 · Answer 12 · 2026-04-13 04:35:42

49

Views

Mapping and Cauchy- Reimann conditions

Published on 13 Apr 2026 - 4:35

score 196 · Answer 13 · 2026-04-14 18:39:41

196

Views

Show $ \int_{0}^{1}\frac{\sin (ax)}{x}dx $ is an entire function.

Published on 14 Apr 2026 - 18:39

score 167 · Answer 14 · 2026-04-08 16:24:36

167

Views

Properties of analytic functions

Published on 08 Apr 2026 - 16:24

score 37 · Answer 15 · 2026-05-10 17:56:12

37

Views

Closed curve for an analityc function

Published on 10 May 2026 - 17:56

List Question

Prove or disprove there is an analytic function $F$ on $\{ 1 < |z| < 2\}$ with $\Re F(x+iy) = \log (x^2+y^2)$

Using Cauchy Riemann complex form to prove Cauchy Riemann polar coordinates form

Domain of analyticity of $f(z) = \frac{1}{z^2}$

Proving that if $f=0$ on an arc or region in $D$, where $f$ is analytic on $D$, than $f = 0$ on $D$.

Extending uniform convergence of analytic functions on larger domains

Express a complex analytic function as a single power series

Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.

For $|q|<1$, the function $\frac{(az;q)_\infty}{(z;q)_\infty}$ is analytic on $|z|<1$.

Properties of Complex Function $f(z)=e^{-\frac{1}{z^{1/3}}}$

Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `

Show that a function is analytic on the punctured complex plane

Mapping and Cauchy- Reimann conditions

Show $ \int_{0}^{1}\frac{\sin (ax)}{x}dx $ is an entire function.

Properties of analytic functions

Closed curve for an analityc function

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