Question

Uniform convergence of a functional series $\sum\limits _{n=1}^{\infty}\frac{x\sin(xn)}{n+x}$

score 157 · Answer 1 · 2026-04-15 11:50:52

157

Views

Uniform convergence of a functional series $\sum\limits _{n=1}^{\infty}\frac{x\sin(xn)}{n+x}$

Published on 15 Apr 2026 - 11:50

score 125 · Answer 2 · 2026-04-14 13:26:18

125

Views

a series of functions that converges uniformly, converges to a harmonic function and so its derivative

Published on 14 Apr 2026 - 13:26

score 46 · Answer 3 · 2026-04-15 18:07:43

46

Views

uniformly convergence of $f_{n}(x)=\frac{n}{2}\int_{x-\frac{1}{n}}^{x+\frac{1}{n}} f(t)dt$?

Published on 15 Apr 2026 - 18:07

score 80 · Answer 4 · 2026-04-17 09:41:33

80

Views

Convergence of sequence of functions $ f_n(x)=\begin{cases} n^{p+1}x & \text{if $0≤x≤1/n$}\\ \frac{1}{x^p} & \text{if $1/n<x≤1$} \end{cases} $

Published on 17 Apr 2026 - 9:41

score 501 · Answer 5 · 2026-04-16 08:55:21

501

Views

Radius of convergence of $\sum_{n=0}^{\infty}\cos(n)z^n$

Published on 16 Apr 2026 - 8:55

score 97 · Answer 6 · 2026-04-15 13:58:21

97

Views

Uniform convergence of $\sum n^\alpha \sin{\frac{x}{n}}$

Published on 15 Apr 2026 - 13:58

score 510 · Answer 7 · 2026-04-16 12:56:13

510

Views

Pointwise and uniform convergence of $f_n(x)=\cos \frac{nx}{1+n^2}$

Published on 16 Apr 2026 - 12:56

score 398 · Answer 8 · 2026-04-16 16:58:26

398

Views

Uniform convergence of sequence of functions on unbounded intervals

Published on 16 Apr 2026 - 16:58

score 632 · Answer 9 · 2026-04-15 10:18:14

632

Views

Is power series $\sum_{n=1}^\infty\frac{x^n}{n}$ uniformly convergent in $(-1,1)$

Published on 15 Apr 2026 - 10:18

score 702 · Answer 10 · 2026-04-18 12:23:27

702

Views

Uniformly Convergent Subsequence of a Pointwise Convergent Sequence of Functions

Published on 18 Apr 2026 - 12:23

score 169 · Answer 11 · 2026-04-16 15:40:55

169

Views

Will $y=x$ and $y=\sin^n \left(\frac{\pi x}{2} \right)$ meet in the interval $(0,1)$ for all $n \ge 2$?

Published on 16 Apr 2026 - 15:40

score 56 · Answer 12 · 2026-04-14 22:31:59

56

Views

Why this answer does not provide counter-example for $C([0,1/2],||\cdot||_\infty)$

Published on 14 Apr 2026 - 22:31

score 49 · Answer 13 · 2026-04-15 10:32:08

49

Views

Uniform convergence of the series $\sum_{n\ge 1}\frac{ne^{-nx}}{1+n^2}$

Published on 15 Apr 2026 - 10:32

score 36 · Answer 14 · 2026-04-12 14:06:49

36

Views

Uniform convergence succession of logarithmic functions

Published on 12 Apr 2026 - 14:06

score 65 · Answer 15 · 2026-04-15 14:10:18

65

Views

Convergence on a Piecewise $f_n$ convergence

Published on 15 Apr 2026 - 14:10

List Question

Uniform convergence of a functional series $\sum\limits _{n=1}^{\infty}\frac{x\sin(xn)}{n+x}$

a series of functions that converges uniformly, converges to a harmonic function and so its derivative

uniformly convergence of $f_{n}(x)=\frac{n}{2}\int_{x-\frac{1}{n}}^{x+\frac{1}{n}} f(t)dt$?

Convergence of sequence of functions $ f_n(x)=\begin{cases} n^{p+1}x & \text{if $0≤x≤1/n$}\\ \frac{1}{x^p} & \text{if $1/n<x≤1$} \end{cases} $

Radius of convergence of $\sum_{n=0}^{\infty}\cos(n)z^n$

Uniform convergence of $\sum n^\alpha \sin{\frac{x}{n}}$

Pointwise and uniform convergence of $f_n(x)=\cos \frac{nx}{1+n^2}$

Uniform convergence of sequence of functions on unbounded intervals

Is power series $\sum_{n=1}^\infty\frac{x^n}{n}$ uniformly convergent in $(-1,1)$

Uniformly Convergent Subsequence of a Pointwise Convergent Sequence of Functions

Will $y=x$ and $y=\sin^n \left(\frac{\pi x}{2} \right)$ meet in the interval $(0,1)$ for all $n \ge 2$?

Why this answer does not provide counter-example for $C([0,1/2],||\cdot||_\infty)$

Uniform convergence of the series $\sum_{n\ge 1}\frac{ne^{-nx}}{1+n^2}$

Uniform convergence succession of logarithmic functions

Convergence on a Piecewise $f_n$ convergence

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