Question

A series of nonanalytic-smooth functions $f'_n = f_{n+1}$ with finite sum?

score 333 · Answer 1 · 2017-10-23 12:10:04

333

Views

A series of nonanalytic-smooth functions $f'_n = f_{n+1}$ with finite sum?

Published on 23 Oct 2017 - 12:10

score 17 · Answer 2 · 2017-10-26 14:09:50

17

Views

Is $g$ analytic in $B(a;r)$?

Published on 26 Oct 2017 - 14:09

score 61 · Answer 3 · 2017-10-27 20:11:07

61

Views

Let $f(x)=(x-a)^{n}g(x)$ such that $g(a)\neq 0$; compute its $n$-th derivative

Published on 27 Oct 2017 - 20:11

score 376 · Answer 4 · 2026-03-29 13:46:59

376

Views

An integral involving a smooth function

Published on 29 Mar 2026 - 13:46

score 65 · Answer 5 · 2017-11-03 03:10:47

65

Views

Analytic Functions at $z_0$

Published on 03 Nov 2017 - 3:10

score 23 · Answer 6 · 2017-11-03 05:18:59

23

Views

Analytic Functions in a set

Published on 03 Nov 2017 - 5:18

score 5k · Answer 7 · 2026-03-25 18:14:32

5k

Views

Deducing the existence of a PDE by constructing it inductively via its Taylor series expansion

Published on 25 Mar 2026 - 18:14

score 205 · Answer 8 · 2026-03-28 21:26:44

205

Views

If $f$ is a continuous analytic function on a unit disc about the origin $D\setminus\{0\}$, then $f$ is also analytic at $0$.

Published on 28 Mar 2026 - 21:26

score 120 · Answer 9 · 2017-11-10 12:36:14

120

Views

Proving a certain behavior of zeros of an analytic function

Published on 10 Nov 2017 - 12:36

score 943 · Answer 10 · 2026-03-28 21:34:25

943

Views

Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$

Published on 28 Mar 2026 - 21:34

score 149 · Answer 11 · 2017-11-14 10:03:17

149

Views

Analytic functions whose all derivatives keep $\mathbb{Z}$ invariant

Published on 14 Nov 2017 - 10:03

score 201 · Answer 12 · 2026-03-25 20:14:18

201

Views

Meromorphic function that preserves the upper half-plane and the lower half plane must have only simple poles, all of them in $\mathbb{R}$

Published on 25 Mar 2026 - 20:14

score 262 · Answer 13 · 2026-03-29 05:50:07

262

Views

Cauchy's integral theorem requirement of open set

Published on 29 Mar 2026 - 5:50

score 32 · Answer 14 · 2017-11-19 04:30:16

32

Views

Let $D=\mathbb{C}\sim(-\infty,0]$. Define $f:D\rightarrow \mathbb{C}$ by $f(z)=(z-1)/Log(z)$ if $z\neq 1$, while $f(1)=1$.

Published on 19 Nov 2017 - 4:30

score 226 · Answer 15 · 2017-11-19 06:00:56

226

Views

Entire Function, Boundary Values $\limsup$, $\liminf$

Published on 19 Nov 2017 - 6:00

List Question

A series of nonanalytic-smooth functions $f'_n = f_{n+1}$ with finite sum?

Is $g$ analytic in $B(a;r)$?

Let $f(x)=(x-a)^{n}g(x)$ such that $g(a)\neq 0$; compute its $n$-th derivative

An integral involving a smooth function

Analytic Functions at $z_0$

Analytic Functions in a set

Deducing the existence of a PDE by constructing it inductively via its Taylor series expansion

If $f$ is a continuous analytic function on a unit disc about the origin $D\setminus\{0\}$, then $f$ is also analytic at $0$.

Proving a certain behavior of zeros of an analytic function

Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$

Analytic functions whose all derivatives keep $\mathbb{Z}$ invariant

Meromorphic function that preserves the upper half-plane and the lower half plane must have only simple poles, all of them in $\mathbb{R}$

Cauchy's integral theorem requirement of open set

Let $D=\mathbb{C}\sim(-\infty,0]$. Define $f:D\rightarrow \mathbb{C}$ by $f(z)=(z-1)/Log(z)$ if $z\neq 1$, while $f(1)=1$.

Entire Function, Boundary Values $\limsup$, $\liminf$

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