List questions from uniform-convergence

Published on 23 Feb 2026 - 2:52

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Prove that lim$_{n \rightarrow \infty} (1 + \frac{z}{n})^{n} = e^z$ uniformly on all compact sets.

Published on 28 Mar 2026 - 8:36

560

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Convergence of $f_n(x)=n^2x(1-x^2)^n$ on $[0,1)$

Published on 15 Jun 2018 - 20:17

385

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Convergence of harmonic functions in $L^1_{loc}$ implies uniform convergence on compact subsets

Published on 25 Mar 2026 - 16:02

3.7k

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Determining convergence of series of exponential functions

Published on 22 Mar 2026 - 1:58

143

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Example of a differentiable $S(x)=\sum f_n(x)$ such that $S'(x)\ne\sum f_n'(x)$ for (at least almost) all x

Published on 26 Mar 2026 - 8:02

561

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Prove that $\sum_{n=0}^\infty\frac{\cos (n^2x)}{2^{nx}}$ is continuous for $x> 0$

Published on 17 Jun 2018 - 11:14

312

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Proof that a sequence converges pointwisely, but not uniformly

Published on 21 Mar 2026 - 21:31

106

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Uniform Convergence and Continuous Functions at Boundary

Published on 17 Jun 2018 - 20:11

243

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the uniform convergence of series (M-test).

Published on 19 Jun 2018 - 4:50

782

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Uniform Convergence of $\frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\frac{8x^7}{1+x^8}+...$

Published on 19 Jun 2018 - 6:30

80

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Uniform convergence for series of functions

Published on 22 Mar 2026 - 14:34

227

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Uniform consistency of a sum of functions with random weights?

Published on 20 Jun 2018 - 9:20

138

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Interchanging limit and integral verification

Published on 20 Jun 2018 - 14:47

160

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Converge uniformly on close interval implies on open interval

Published on 21 Jun 2018 - 8:22

List Question

Uniform convergence on two separate intervals

Prove that lim$_{n \rightarrow \infty} (1 + \frac{z}{n})^{n} = e^z$ uniformly on all compact sets.

Convergence of $f_n(x)=n^2x(1-x^2)^n$ on $[0,1)$

Convergence of harmonic functions in $L^1_{loc}$ implies uniform convergence on compact subsets

Determining convergence of series of exponential functions

Example of a differentiable $S(x)=\sum f_n(x)$ such that $S'(x)\ne\sum f_n'(x)$ for (at least almost) all x

Prove that $\sum_{n=0}^\infty\frac{\cos (n^2x)}{2^{nx}}$ is continuous for $x> 0$

Proof that a sequence converges pointwisely, but not uniformly

Uniform Convergence and Continuous Functions at Boundary

the uniform convergence of series (M-test).

Uniform Convergence of $\frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\frac{8x^7}{1+x^8}+...$

Uniform convergence for series of functions

Uniform consistency of a sum of functions with random weights?

Interchanging limit and integral verification

Converge uniformly on close interval implies on open interval

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