Question

Does $\int_{0}^{\infty} \frac{\sin(x)}{x} e^{-\alpha x}dx$ converge uniformly?

score 169 · Answer 1 · 2026-04-15 03:39:48

169

Views

Does $\int_{0}^{\infty} \frac{\sin(x)}{x} e^{-\alpha x}dx$ converge uniformly?

Published on 15 Apr 2026 - 3:39

score 98 · Answer 2 · 2026-04-15 18:07:29

98

Views

Uniform convergence of the integral $\int_{0}^{\pi} \frac{\sin(x)}{x^{\alpha}(\pi -x)^{\alpha}} dx$ with $0 < \alpha < 2$

Published on 15 Apr 2026 - 18:07

score 270 · Answer 3 · 2026-04-14 04:24:48

270

Views

Pointwise and uniform convergence of power series

Published on 14 Apr 2026 - 4:24

score 72 · Answer 4 · 2026-04-16 00:21:33

72

Views

Pointwise and uniform convergence of ${\sum_{n=1}^{+\infty}\left (1+\frac{1}{2n}\right )^{4n^2}x^n}$

Published on 16 Apr 2026 - 0:21

score 108 · Answer 5 · 2026-04-13 09:11:58

108

Views

Show the equivalence between two negations of uniformly convergence.

Published on 13 Apr 2026 - 9:11

score 123 · Answer 6 · 2026-04-13 09:07:08

123

Views

converging sequence of continuous functions

Published on 13 Apr 2026 - 9:07

score 96 · Answer 7 · 2026-04-16 20:45:06

96

Views

Convergence of sequence of curves from convergence of tangent vectors

Published on 16 Apr 2026 - 20:45

score 195 · Answer 8 · 2026-04-12 05:32:11

195

Views

Is it possible to interchange sum and integral when the series doesn't converge uniformly?

Published on 12 Apr 2026 - 5:32

score 225 · Answer 9 · 2026-04-15 04:44:58

225

Views

Creating an epsilon of room to prove convergence in mean

Published on 15 Apr 2026 - 4:44

score 112 · Answer 10 · 2026-04-16 00:56:00

112

Views

Let $g_n(x)= g(x+\frac{1}{n})$. Prove that $(g_n)$ converges uniformly to $g$.

Published on 16 Apr 2026 - 0:56

score 118 · Answer 11 · 2026-04-13 16:52:47

118

Views

Prove a nested sequence of functions converges pointwise but it doesnt converges uniformly.

Published on 13 Apr 2026 - 16:52

score 113 · Answer 12 · 2026-04-17 04:32:45

113

Views

Prove that the sequence of functions $f_n(x)=x^ng(x), n \in \mathbb{N}$, converge uniformly on $[0, 1]$.

Published on 17 Apr 2026 - 4:32

score 931 · Answer 13 · 2026-04-16 01:50:57

931

Views

Do power series converge uniformly and absolutely on radius of convergence?

Published on 16 Apr 2026 - 1:50

score 72 · Answer 14 · 2026-04-11 01:57:35

72

Views

What functions can have uniformly convergent sequences of derivatives?

Published on 11 Apr 2026 - 1:57

score 422 · Answer 15 · 2026-04-14 02:28:45

422

Views

Uniform convergence of power series expansion of a holomorphic function

Published on 14 Apr 2026 - 2:28

List Question

Does $\int_{0}^{\infty} \frac{\sin(x)}{x} e^{-\alpha x}dx$ converge uniformly?

Uniform convergence of the integral $\int_{0}^{\pi} \frac{\sin(x)}{x^{\alpha}(\pi -x)^{\alpha}} dx$ with $0 < \alpha < 2$

Pointwise and uniform convergence of power series

Pointwise and uniform convergence of ${\sum_{n=1}^{+\infty}\left (1+\frac{1}{2n}\right )^{4n^2}x^n}$

Show the equivalence between two negations of uniformly convergence.

converging sequence of continuous functions

Convergence of sequence of curves from convergence of tangent vectors

Is it possible to interchange sum and integral when the series doesn't converge uniformly?

Creating an epsilon of room to prove convergence in mean

Let $g_n(x)= g(x+\frac{1}{n})$. Prove that $(g_n)$ converges uniformly to $g$.

Prove a nested sequence of functions converges pointwise but it doesnt converges uniformly.

Prove that the sequence of functions $f_n(x)=x^ng(x), n \in \mathbb{N}$, converge uniformly on $[0, 1]$.

Do power series converge uniformly and absolutely on radius of convergence?

What functions can have uniformly convergent sequences of derivatives?

Uniform convergence of power series expansion of a holomorphic function

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