Question

Uniform convergence of holomorphic functions

score 90 · Answer 1 · 2023-06-28 05:40:36

90

Views

Uniform convergence of holomorphic functions

Published on 28 Jun 2023 - 5:40

score 42 · Answer 2 · 2023-07-01 08:46:43

42

Views

Why does $\sum_{n=1}^\infty (-1)^nx^n(1-x) $ not have a convergent majorant series?

Published on 01 Jul 2023 - 8:46

score 32 · Answer 3 · 2023-07-02 12:42:16

I wonder why the author didn't assume that $f,f_1,f_2,\dots$ are bounded functions. Any reason? ("Introduction to Analysis I" by Mitsuo Sugiura)

score 98 · Answer 4 · 2023-07-02 23:21:04

98

Views

Check the uniform convergence of $f_n=\frac{n}{nx^{2}+1}$ on $[\frac12,\infty)$ and $(0,\infty)$

Published on 02 Jul 2023 - 23:21

score 66 · Answer 5 · 2026-02-25 02:34:59

66

Views

I wonder why the author assumed $(f_n)_{n\in\mathbb{N}}$ converges pointwise to a function $f$ on $[a,b]$. ("Calculus I" by Shizuo Miyazima)

Published on 25 Feb 2026 - 2:34

score 40 · Answer 6 · 2023-07-03 19:34:21

40

Views

Necessary condition for switching the order of limit and differentiation

Published on 03 Jul 2023 - 19:34

score 111 · Answer 7 · 2023-07-06 19:58:08

111

Views

Prove that $\sum_k f'_k$ converges to $f'$ a.e on $[a,b]$.

Published on 06 Jul 2023 - 19:58

score 58 · Answer 8 · 2026-02-24 17:16:26

58

Views

Uniform convergence of $\sin(nx) \cdot\frac{x}{n} + x$

Published on 24 Feb 2026 - 17:16

score 55 · Answer 9 · 2026-02-25 02:33:25

55

Views

Can the monotonicity criterion be dropped from the Abel's Test for Uniform convergence?

Published on 25 Feb 2026 - 2:33

score 84 · Answer 10 · 2023-07-08 08:57:39

84

Views

If $f_n,g_n: [0,1] \to [0,1]$ continuous $\forall n \in \mathbb{N}$ and converge uniformly prove that $f_n \circ g_n \xrightarrow{u.c} f\circ g$

Published on 08 Jul 2023 - 8:57

score 55 · Answer 11 · 2026-03-28 02:48:24

55

Views

Series, sum uniform convergence

Published on 28 Mar 2026 - 2:48

score 30 · Answer 12 · 2026-04-01 16:20:09

30

Views

Proof of uniform convergence (specific case)

Published on 01 Apr 2026 - 16:20

score 62 · Answer 13 · 2023-07-12 23:28:56

62

Views

Finding out where a complex function is holomorphic and relating this to its expansion as a power series.

Published on 12 Jul 2023 - 23:28

score 78 · Answer 14 · 2023-07-16 12:22:36

78

Views

Contrapositive of uniform limit theorem for series

Published on 16 Jul 2023 - 12:22

score 77 · Answer 15 · 2026-02-23 10:46:14

77

Views

Class of Lipschitz Functions on the unit d-dimensional ball

Published on 23 Feb 2026 - 10:46

List Question

Uniform convergence of holomorphic functions

Why does $\sum_{n=1}^\infty (-1)^nx^n(1-x) $ not have a convergent majorant series?

I wonder why the author didn't assume that $f,f_1,f_2,\dots$ are bounded functions. Any reason? ("Introduction to Analysis I" by Mitsuo Sugiura)

Check the uniform convergence of $f_n=\frac{n}{nx^{2}+1}$ on $[\frac12,\infty)$ and $(0,\infty)$

I wonder why the author assumed $(f_n)_{n\in\mathbb{N}}$ converges pointwise to a function $f$ on $[a,b]$. ("Calculus I" by Shizuo Miyazima)

Necessary condition for switching the order of limit and differentiation

Prove that $\sum_k f'_k$ converges to $f'$ a.e on $[a,b]$.

Uniform convergence of $\sin(nx) \cdot\frac{x}{n} + x$

Can the monotonicity criterion be dropped from the Abel's Test for Uniform convergence?

If $f_n,g_n: [0,1] \to [0,1]$ continuous $\forall n \in \mathbb{N}$ and converge uniformly prove that $f_n \circ g_n \xrightarrow{u.c} f\circ g$

Series, sum uniform convergence

Proof of uniform convergence (specific case)

Finding out where a complex function is holomorphic and relating this to its expansion as a power series.

Contrapositive of uniform limit theorem for series

Class of Lipschitz Functions on the unit d-dimensional ball

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