List questions from uniform-convergence

Published on 21 Jun 2018 - 19:01

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Prove $f_n(x) = n^2 x (1-x)^n$ does not converges uniformly

Published on 21 Jun 2018 - 22:27

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$\alpha$ for uniform convergence $\sum \frac{x^\alpha}{1+n^2x^2}$

Published on 22 Jun 2018 - 16:38

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Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $[0,1)$?

Published on 23 Jun 2018 - 19:09

366

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Residue identity for function composition: $ \operatorname{Res}(f; h(a)) = \operatorname{Res}((f∘h)h'; a)$

Published on 26 Mar 2026 - 19:20

110

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How do you memorize Abel and Dirichlet convergence criterions?

Published on 26 Mar 2026 - 22:13

97

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A question about Egoroff theorem

Published on 25 Jun 2018 - 18:16

247

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Convergence and compactness of $f_n(t) = \sin (\sqrt{t + 4n^2\pi})$.

Published on 27 Jun 2018 - 23:18

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If $f_m \rightarrow f$ in $L^p$, does $|f_m|^r \rightarrow |f|^r$ in $L^{\frac{p}{r}}$?

Published on 26 Mar 2026 - 0:53

279

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Weierstrass M-test with functions instead of numbers as bounds

Published on 29 Jun 2018 - 21:20

94

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Show that $\int_{-\infty}^{\infty}(1+\frac{x^2}{n})^{-n}dx\rightarrow \int_{-\infty}^{\infty} e^{-x^2}dx$

Published on 28 Mar 2026 - 7:00

66

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uniform converges and compact sets

Published on 03 Jul 2018 - 22:56

143

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Uniform limit of functions with intermediate value property has intermediate value property? Where is the error in this proof?

Published on 25 Mar 2026 - 7:48

592

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prove that if a series of functions converges uniformly in D...

Published on 23 Feb 2026 - 4:56

100

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Uniform Convergent and term by term differentiation

Published on 10 Jul 2018 - 8:03

List Question

Uniform Convergence $\sum \frac{x}{n(1+nx^2)}$

Prove $f_n(x) = n^2 x (1-x)^n$ does not converges uniformly

$\alpha$ for uniform convergence $\sum \frac{x^\alpha}{1+n^2x^2}$

Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $[0,1)$?

Residue identity for function composition: $ \operatorname{Res}(f; h(a)) = \operatorname{Res}((f∘h)h'; a)$

How do you memorize Abel and Dirichlet convergence criterions?

A question about Egoroff theorem

Convergence and compactness of $f_n(t) = \sin (\sqrt{t + 4n^2\pi})$.

If $f_m \rightarrow f$ in $L^p$, does $|f_m|^r \rightarrow |f|^r$ in $L^{\frac{p}{r}}$?

Weierstrass M-test with functions instead of numbers as bounds

Show that $\int_{-\infty}^{\infty}(1+\frac{x^2}{n})^{-n}dx\rightarrow \int_{-\infty}^{\infty} e^{-x^2}dx$

uniform converges and compact sets

Uniform limit of functions with intermediate value property has intermediate value property? Where is the error in this proof?

prove that if a series of functions converges uniformly in D...

Uniform Convergent and term by term differentiation

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