Question

Smooth sequence of functions converging pointwise to a smooth function and limit of derivatives

score 930 · Answer 1 · 2026-04-14 12:46:10

930

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Smooth sequence of functions converging pointwise to a smooth function and limit of derivatives

Published on 14 Apr 2026 - 12:46

score 286 · Answer 2 · 2026-04-16 15:14:22

286

Views

Compute the limit of $\displaystyle\lim_{n \to \infty} \int_0^1 \frac{e^{-nt}}{\sqrt{t}} \, dt$

Published on 16 Apr 2026 - 15:14

score 48 · Answer 3 · 2026-04-12 00:09:19

48

Views

Is there a relation between weak-* convergence in $L^\infty((0,T); L^2(\Omega))$ and strong convergence in $L^2(\Omega)$ uniformly in $t$?

Published on 12 Apr 2026 - 0:09

score 37 · Answer 4 · 2026-04-14 10:26:08

37

Views

Showing failure of uniform convergence

Published on 14 Apr 2026 - 10:26

score 68 · Answer 5 · 2026-04-16 18:51:18

68

Views

Does the sequence $\displaystyle g_n(t)=\int_0^1 \frac{t f(\sqrt[n]{x})}{1+t f(\sqrt[n]{x})} dx$ converge uniformly on $[0, \infty)$?

Published on 16 Apr 2026 - 18:51

score 558 · Answer 6 · 2026-04-17 23:08:00

558

Views

Uniform convergence of a series of functions with cos(x)

Published on 17 Apr 2026 - 23:08

score 138 · Answer 7 · 2026-04-18 04:27:29

138

Views

Point wise convergence and differentiation counter examples

Published on 18 Apr 2026 - 4:27

score 52 · Answer 8 · 2026-04-14 09:01:11

52

Views

Uniform convergence of series with nonnegative terms implies uniform convergence of terms to zero

Published on 14 Apr 2026 - 9:01

score 76 · Answer 9 · 2026-04-11 17:19:52

76

Views

Continuous extension in the proof of Arzela - Ascoli theorem

Published on 11 Apr 2026 - 17:19

score 229 · Answer 10 · 2026-04-17 03:35:53

229

Views

Check if $\left\{\frac{1}{z^2+\frac 1 n}\right\}_{n=1}^{\infty}$ is uniform (or at least pointwise) convergent.

Published on 17 Apr 2026 - 3:35

score 73 · Answer 11 · 2026-04-15 18:09:48

73

Views

Complex non-/uniform convergence: About dependence of the index $N$ on modulus $|z|$ vs complex number $z$

Published on 15 Apr 2026 - 18:09

score 62 · Answer 12 · 2026-04-15 16:35:59

62

Views

Use Weierstrass m-test to establish uniform convergence of geometric series: What is the relation between $\{|z| \le 3.5\}$ and $\{|z+5|>1\}$?

Published on 15 Apr 2026 - 16:35

score 164 · Answer 13 · 2026-04-17 00:44:24

164

Views

Showing uniform convergence of $\frac{x}{1+n^2x^2}$

Published on 17 Apr 2026 - 0:44

score 78 · Answer 14 · 2026-04-14 21:02:11

78

Views

Showing that $\frac{1}{f_n} \to \frac{1}{f}$ uniformly

Published on 14 Apr 2026 - 21:02

score 79 · Answer 15 · 2026-04-14 20:44:35

79

Views

Relation between two notions intermediate between “pointwise convergence” and “uniform convergence”

Published on 14 Apr 2026 - 20:44

List Question

Smooth sequence of functions converging pointwise to a smooth function and limit of derivatives

Compute the limit of $\displaystyle\lim_{n \to \infty} \int_0^1 \frac{e^{-nt}}{\sqrt{t}} \, dt$

Is there a relation between weak-* convergence in $L^\infty((0,T); L^2(\Omega))$ and strong convergence in $L^2(\Omega)$ uniformly in $t$?

Showing failure of uniform convergence

Does the sequence $\displaystyle g_n(t)=\int_0^1 \frac{t f(\sqrt[n]{x})}{1+t f(\sqrt[n]{x})} dx$ converge uniformly on $[0, \infty)$?

Uniform convergence of a series of functions with cos(x)

Point wise convergence and differentiation counter examples

Uniform convergence of series with nonnegative terms implies uniform convergence of terms to zero

Continuous extension in the proof of Arzela - Ascoli theorem

Check if $\left\{\frac{1}{z^2+\frac 1 n}\right\}_{n=1}^{\infty}$ is uniform (or at least pointwise) convergent.

Complex non-/uniform convergence: About dependence of the index $N$ on modulus $|z|$ vs complex number $z$

Use Weierstrass m-test to establish uniform convergence of geometric series: What is the relation between $\{|z| \le 3.5\}$ and $\{|z+5|>1\}$?

Showing uniform convergence of $\frac{x}{1+n^2x^2}$

Showing that $\frac{1}{f_n} \to \frac{1}{f}$ uniformly

Relation between two notions intermediate between “pointwise convergence” and “uniform convergence”

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