List questions from convergence-divergence

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convergence modes

Published on 26 Mar 2026 - 4:48

274

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Complex generating function for Legendre polynomials

Published on 24 Mar 2026 - 22:10

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What is the rate of convergence of $f^N(x) = \sum_{n=-N}^N f_n e^{in x}$ to $f(x) = \sum_{n=-\infty}^\infty f_n e^{in x}$ in $L^2([0,2\pi])$?

Published on 25 Mar 2026 - 17:44

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Can we approximates any real continuous function on a compact $[0,T]$ by a step function uniformly?

Published on 28 Mar 2026 - 6:58

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The set of all probability measures on $(\Xi,\mathcal{B})$ is weakly compact with respect to topology of total variation?

Published on 04 Jun 2018 - 4:57

227

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How to show pointwise and uniform convergence of specific series

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Convergence in distribution of independent random variables

Published on 04 Jun 2018 - 14:03

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Comparison test on $ \int_2 ^\infty \frac{\ln(t)}{t^{3/2}} \ dt$

Published on 04 Jun 2018 - 14:30

154

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Convergence in distribution and convergence of variance

Published on 02 Apr 2026 - 20:14

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$ \int_2^{\infty}\frac{1}{x\sqrt{x^2-4}}dx$ convergence verification

Published on 04 Jun 2018 - 14:48

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Limits of two variables $\lim_{t \rightarrow \infty} \lim_{u \rightarrow t} u^{\alpha} \sqrt{t-u} = 0$

Published on 04 Jun 2018 - 14:58

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Sufficient condition for convergence in probability to imply convergence in $L^1$

Published on 04 Jun 2018 - 22:12

450

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Abel's theorem infinite case

Published on 27 Mar 2026 - 6:51

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Using the Cauchy root test

Published on 27 Mar 2026 - 8:47

List Question

Convergence Test (Ratio Test) for $\sum_n \frac{(2n)!}{n^{2n}}$

convergence modes

Complex generating function for Legendre polynomials

What is the rate of convergence of $f^N(x) = \sum_{n=-N}^N f_n e^{in x}$ to $f(x) = \sum_{n=-\infty}^\infty f_n e^{in x}$ in $L^2([0,2\pi])$?

Can we approximates any real continuous function on a compact $[0,T]$ by a step function uniformly?

The set of all probability measures on $(\Xi,\mathcal{B})$ is weakly compact with respect to topology of total variation?

How to show pointwise and uniform convergence of specific series

Convergence in distribution of independent random variables

Comparison test on $ \int_2 ^\infty \frac{\ln(t)}{t^{3/2}} \ dt$

Convergence in distribution and convergence of variance

$ \int_2^{\infty}\frac{1}{x\sqrt{x^2-4}}dx$ convergence verification

Limits of two variables $\lim_{t \rightarrow \infty} \lim_{u \rightarrow t} u^{\alpha} \sqrt{t-u} = 0$

Sufficient condition for convergence in probability to imply convergence in $L^1$

Abel's theorem infinite case

Using the Cauchy root test

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