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 64 · Answer 1 · 2018-10-24 20:54:33

64

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 24 Oct 2018 - 20:54

score 653 · Answer 2 · 2018-10-25 19:20:15

653

Views

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

Published on 25 Oct 2018 - 19:20

score 3.6k · Answer 3 · 2018-10-25 20:35:51

3.6k

Views

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

Published on 25 Oct 2018 - 20:35

score 111 · Answer 4 · 2018-10-29 09:12:28

111

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 29 Oct 2018 - 9:12

score 56 · Answer 5 · 2018-11-05 23:02:09

56

Views

Extending uniform convergence of analytic functions on larger domains

Published on 05 Nov 2018 - 23:02

score 81 · Answer 6 · 2018-11-08 13:22:38

81

Views

Express a complex analytic function as a single power series

Published on 08 Nov 2018 - 13:22

score 1.8k · Answer 7 · 2018-11-09 00:02:26

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 09 Nov 2018 - 0:02

score 53 · Answer 8 · 2026-03-25 00:55:17

53

Views

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

Published on 25 Mar 2026 - 0:55

score 57 · Answer 9 · 2026-03-25 04:40:11

57

Views

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

Published on 25 Mar 2026 - 4:40

score 543 · Answer 10 · 2018-11-11 22:44:57

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 66 · Answer 11 · 2018-11-12 23:30:26

66

Views

Show that a function is analytic on the punctured complex plane

Published on 12 Nov 2018 - 23:30

score 46 · Answer 12 · 2018-11-14 06:22:16

46

Views

Mapping and Cauchy- Reimann conditions

Published on 14 Nov 2018 - 6:22

score 193 · Answer 13 · 2018-11-16 14:53:22

193

Views

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

Published on 16 Nov 2018 - 14:53

score 164 · Answer 14 · 2018-11-17 00:07:39

164

Views

Properties of analytic functions

Published on 17 Nov 2018 - 0:07

score 35 · Answer 15 · 2026-03-25 04:34:59

35

Views

Closed curve for an analityc function

Published on 25 Mar 2026 - 4:34

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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