Question

Equivalence of compact and uniform convergence for sequences of holomorphic functions

score 67 · Answer 1 · 2026-04-14 08:44:28

67

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Equivalence of compact and uniform convergence for sequences of holomorphic functions

Published on 14 Apr 2026 - 8:44

score 119 · Answer 2 · 2026-04-16 01:00:40

119

Views

Limit of holomorphic and bounded functions that can be extended to a ball

Published on 16 Apr 2026 - 1:00

score 834 · Answer 3 · 2026-04-11 13:14:00

834

Views

Does there exist a sequence of polynomials converging uniformly to $f(x) = |x| $ on $ℝ$?

Published on 11 Apr 2026 - 13:14

score 74 · Answer 4 · 2026-04-17 04:54:06

74

Views

Uniform convergence of $f_n(x)=\frac{x^n}{n!}$

Published on 17 Apr 2026 - 4:54

score 602 · Answer 5 · 2026-04-16 23:05:22

602

Views

What does point-wise convergence in the sup norm mean?

Published on 16 Apr 2026 - 23:05

score 98 · Answer 6 · 2026-04-14 09:50:59

98

Views

Convergence and differentiability of a power series

Published on 14 Apr 2026 - 9:50

score 46 · Answer 7 · 2026-04-17 05:29:37

46

Views

proving uniform convergence and differentiability for any bounded open interval ($a,b$) $\in \mathbb{R}$

Published on 17 Apr 2026 - 5:29

score 74 · Answer 8 · 2026-04-17 09:11:25

74

Views

Uniform convergence of a Mollifier Sequence $f_{\rho}:=g_{\rho}*f$

Published on 17 Apr 2026 - 9:11

score 111 · Answer 9 · 2026-04-15 17:10:05

111

Views

Bounding the uniform deviation of the empirical risk from the risk over a finite function class.

Published on 15 Apr 2026 - 17:10

score 324 · Answer 10 · 2026-04-15 18:11:30

324

Views

Prove the power series $ \sum_{k=1}^{\infty} \frac{x^{k}}{k(k+1)} $ converges uniformly on $-1 \leq x \leq 1$.

Published on 15 Apr 2026 - 18:11

score 95 · Answer 11 · 2026-04-16 11:23:27

95

Views

$\lim_{n \to \infty}({ \int_{0}^{1}{f_n(x)\,dx}) }=0$ and $\lim_{n \to \infty}({ \int_{0}^{1}{exp((f_n(x))\,dx)} }=0$ are true?

Published on 16 Apr 2026 - 11:23

score 68 · Answer 12 · 2026-04-17 04:05:46

68

Views

$\lim_{n \to \infty} f_{n}(x_{n})=f(a)$

Published on 17 Apr 2026 - 4:05

score 103 · Answer 13 · 2026-04-18 13:49:09

103

Views

Showing Uniform Continuity of An Infinite Series and Termwise Differentiation

Published on 18 Apr 2026 - 13:49

score 85 · Answer 14 · 2026-04-15 21:11:33

85

Views

Uniform Convergence of $f_n(x) = \frac{n(1-2x) + \cos x -x\sin^2 x}{2n + \sin^2 x}$ [proof verification]

Published on 15 Apr 2026 - 21:11

score 72 · Answer 15 · 2026-04-15 10:20:10

72

Views

Convergence in distribution $\sqrt{n}X_n \xrightarrow{n \to +\infty} \mathcal{N}(0,1)$ implies $\sup_{n\in \Bbb N^*}E(|X_n|)<+\infty$

Published on 15 Apr 2026 - 10:20

List Question

Equivalence of compact and uniform convergence for sequences of holomorphic functions

Limit of holomorphic and bounded functions that can be extended to a ball

Does there exist a sequence of polynomials converging uniformly to $f(x) = |x| $ on $ℝ$?

Uniform convergence of $f_n(x)=\frac{x^n}{n!}$

What does point-wise convergence in the sup norm mean?

Convergence and differentiability of a power series

proving uniform convergence and differentiability for any bounded open interval ($a,b$) $\in \mathbb{R}$

Uniform convergence of a Mollifier Sequence $f_{\rho}:=g_{\rho}*f$

Bounding the uniform deviation of the empirical risk from the risk over a finite function class.

Prove the power series $ \sum_{k=1}^{\infty} \frac{x^{k}}{k(k+1)} $ converges uniformly on $-1 \leq x \leq 1$.

$\lim_{n \to \infty}({ \int_{0}^{1}{f_n(x)\,dx}) }=0$ and $\lim_{n \to \infty}({ \int_{0}^{1}{exp((f_n(x))\,dx)} }=0$ are true?

$\lim_{n \to \infty} f_{n}(x_{n})=f(a)$

Showing Uniform Continuity of An Infinite Series and Termwise Differentiation

Uniform Convergence of $f_n(x) = \frac{n(1-2x) + \cos x -x\sin^2 x}{2n + \sin^2 x}$ [proof verification]

Convergence in distribution $\sqrt{n}X_n \xrightarrow{n \to +\infty} \mathcal{N}(0,1)$ implies $\sup_{n\in \Bbb N^*}E(|X_n|)<+\infty$

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