Question

Prove that $\int_0^\infty \int_0^\infty e^{-xy}(\sin x)\,dy\,dx=\int_0^{\infty}\int_0^{\infty}e^{-xy}(\sin x)\,dx\,dy$.

score 2.6k · Answer 1 · 2015-10-07 08:42:18

2.6k

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Prove that $\int_0^\infty \int_0^\infty e^{-xy}(\sin x)\,dy\,dx=\int_0^{\infty}\int_0^{\infty}e^{-xy}(\sin x)\,dx\,dy$.

Published on 07 Oct 2015 - 8:42

score 51 · Answer 2 · 2026-04-09 12:33:15

51

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The definition of Pointwise Convergence{Analysis}

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score 354 · Answer 3 · 2026-04-12 14:53:36

354

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Criteria for convergence in $L^1$ for sigma finite measure

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score 3.2k · Answer 4 · 2015-10-12 20:33:40

3.2k

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Example of a sequence that is not Cauchy

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score 1k · Answer 5 · 2026-03-21 20:09:01

1k

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Uniform Convergence using Abel's test for a series based on convergence of a series

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score 331 · Answer 6 · 2015-10-14 20:03:28

331

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Uniform convergence and differentiation proof

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score 868 · Answer 7 · 2026-03-12 06:31:40

868

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Study the convergence of a succession of functions

Published on 12 Mar 2026 - 6:31

score 37 · Answer 8 · 2015-10-19 08:56:42

37

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Weierstrass M-test: Do the terms of the M-series have to be the same constants?

Published on 19 Oct 2015 - 8:56

score 177 · Answer 9 · 2015-10-20 12:32:17

177

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Show $f_n(x_n) \to f(x)$ if $f_n \to f$ uniformly and $x_n \to x$.

Published on 20 Oct 2015 - 12:32

score 63 · Answer 10 · 2026-02-23 09:13:23

63

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What is convergence interval of $ \sum_{n=1}^\infty a^{\sqrt{n}} \cdot x^n$ where $a \in (0,1)?$

Published on 23 Feb 2026 - 9:13

score 62 · Answer 11 · 2015-10-21 10:34:35

62

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Show that $\displaystyle f_n(x) = \frac{x}{1+n^2x^2}$ converges uniformly to $0$ on $[0, \infty)$

Published on 21 Oct 2015 - 10:34

score 1.3k · Answer 12 · 2015-10-21 15:12:42

1.3k

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Prove the the power series converge uniformly

Published on 21 Oct 2015 - 15:12

score 3.7k · Answer 13 · 2015-10-21 19:23:47

3.7k

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Show that $N\sum_{n = 2}^{\infty} \frac{t^n}{nN^n}$ converges uniformly to $0$

Published on 21 Oct 2015 - 19:23

score 4.2k · Answer 14 · 2015-10-22 11:28:26

4.2k

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Uniform convergence on closed interval

Published on 22 Oct 2015 - 11:28

score 1.2k · Answer 15 · 2015-10-22 17:03:26

1.2k

Views

Determine whether the series converges uniformly

Published on 22 Oct 2015 - 17:03

List Question

Prove that $\int_0^\infty \int_0^\infty e^{-xy}(\sin x)\,dy\,dx=\int_0^{\infty}\int_0^{\infty}e^{-xy}(\sin x)\,dx\,dy$.

The definition of Pointwise Convergence{Analysis}

Criteria for convergence in $L^1$ for sigma finite measure

Example of a sequence that is not Cauchy

Uniform Convergence using Abel's test for a series based on convergence of a series

Uniform convergence and differentiation proof

Study the convergence of a succession of functions

Weierstrass M-test: Do the terms of the M-series have to be the same constants?

Show $f_n(x_n) \to f(x)$ if $f_n \to f$ uniformly and $x_n \to x$.

What is convergence interval of $ \sum_{n=1}^\infty a^{\sqrt{n}} \cdot x^n$ where $a \in (0,1)?$

Show that $\displaystyle f_n(x) = \frac{x}{1+n^2x^2}$ converges uniformly to $0$ on $[0, \infty)$

Prove the the power series converge uniformly

Show that $N\sum_{n = 2}^{\infty} \frac{t^n}{nN^n}$ converges uniformly to $0$

Uniform convergence on closed interval

Determine whether the series converges uniformly

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