Question

$(f(z+h) - f(z))/h$ converges uniformly as $h \to 0$

score 69 · Answer 1 · 2023-03-20 16:15:24

69

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$(f(z+h) - f(z))/h$ converges uniformly as $h \to 0$

Published on 20 Mar 2023 - 16:15

score 127 · Answer 2 · 2023-03-20 22:19:51

127

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Uniform convergence of $\sum_{n=1}^\infty x \sin\frac{1}{x^2n^2}$, $x \in (0,+\infty)$

Published on 20 Mar 2023 - 22:19

score 43 · Answer 3 · 2023-03-21 12:57:55

43

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Show that $f_n(x) = \frac{\sqrt{n}x}{1+nx+n^2 x^3}$ does not converge in C([0,1]) with the $\sup$ norm

Published on 21 Mar 2023 - 12:57

score 190 · Answer 4 · 2026-04-08 02:26:47

190

Views

Applying Fundamental Theorem of Calculus to improper integral

Published on 08 Apr 2026 - 2:26

score 45 · Answer 5 · 2026-03-30 08:58:55

45

Views

Local Uniform Convergence of a series of modified Bessel functions of the first kind

Published on 30 Mar 2026 - 8:58

score 101 · Answer 6 · 2023-03-22 06:40:49

101

Views

There is $R > 0$ such that there are no holomorphic functions $f: \{z: |z| < R \} \to \mathbb C \backslash \{0,1\}$ with $f(0) = a$ and $f'(0)= b$

Published on 22 Mar 2023 - 6:40

score 151 · Answer 7 · 2026-03-30 03:24:53

151

Views

$(\beta_n)_{n \geq 0}$ converges uniformly to the solution of $x' = F(t,x)$, variation of Picard iteration?

Published on 30 Mar 2026 - 3:24

score 233 · Answer 8 · 2026-03-30 20:52:55

233

Views

Convergence of the central limit theorem: pointwise vs uniform convergence

Published on 30 Mar 2026 - 20:52

score 130 · Answer 9 · 2023-03-24 16:43:02

130

Views

Integral of sequences of piecewise functions.

Published on 24 Mar 2023 - 16:43

score 35 · Answer 10 · 2026-02-23 13:44:29

35

Views

Uniform convergence, Pointwise Equicontinuity and Uniform Equicontinuity for functon.

Published on 23 Feb 2026 - 13:44

score 46 · Answer 11 · 2026-02-24 13:38:16

46

Views

Pointwise convergence of $f_n$

Published on 24 Feb 2026 - 13:38

score 126 · Answer 12 · 2026-03-25 02:31:33

126

Views

Calculating a limit of a sequence of integrals that approaches the catalan constant

Published on 25 Mar 2026 - 2:31

score 31 · Answer 13 · 2023-04-02 00:52:10

31

Views

Continuous version of uniform continuity?

Published on 02 Apr 2023 - 0:52

score 403 · Answer 14 · 2026-02-24 23:14:25

403

Views

Uniformly convergent on compact interval

Published on 24 Feb 2026 - 23:14

score 60 · Answer 15 · 2023-04-04 13:12:40

60

Views

Does $ \sum_{k=0}^{\infty} a_k s_k(t) $, where $s_k$ is the $k$-th Schauder function, converge unconditionally?

Published on 04 Apr 2023 - 13:12

List Question

$(f(z+h) - f(z))/h$ converges uniformly as $h \to 0$

Uniform convergence of $\sum_{n=1}^\infty x \sin\frac{1}{x^2n^2}$, $x \in (0,+\infty)$

Show that $f_n(x) = \frac{\sqrt{n}x}{1+nx+n^2 x^3}$ does not converge in C([0,1]) with the $\sup$ norm

Applying Fundamental Theorem of Calculus to improper integral

Local Uniform Convergence of a series of modified Bessel functions of the first kind

There is $R > 0$ such that there are no holomorphic functions $f: \{z: |z| < R \} \to \mathbb C \backslash \{0,1\}$ with $f(0) = a$ and $f'(0)= b$

$(\beta_n)_{n \geq 0}$ converges uniformly to the solution of $x' = F(t,x)$, variation of Picard iteration?

Convergence of the central limit theorem: pointwise vs uniform convergence

Integral of sequences of piecewise functions.

Uniform convergence, Pointwise Equicontinuity and Uniform Equicontinuity for functon.

Pointwise convergence of $f_n$

Calculating a limit of a sequence of integrals that approaches the catalan constant

Continuous version of uniform continuity?

Uniformly convergent on compact interval

Does $ \sum_{k=0}^{\infty} a_k s_k(t) $, where $s_k$ is the $k$-th Schauder function, converge unconditionally?

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