Question

How to compute $\parallel f \parallel_{L_2(\mathbb{R}^2)}$ for $f(x,y)=\frac{1}{1+(x-y)^2}$?

score 45 · Answer 1 · 2020-05-27 11:56:15

45

Views

How to compute $\parallel f \parallel_{L_2(\mathbb{R}^2)}$ for $f(x,y)=\frac{1}{1+(x-y)^2}$?

Published on 27 May 2020 - 11:56

score 730 · Answer 2 · 2026-03-30 11:57:14

730

Views

Evaluate a real integral, e.g. $\int_{0}^{\infty}\frac{x^2}{(x^2+1)(x^2+4)}\:\mathrm dx$ with complex analysis

Published on 30 Mar 2026 - 11:57

score 311 · Answer 3 · 2026-03-30 20:16:57

311

Views

Calculating $\Gamma (n+5/2)$

Published on 30 Mar 2026 - 20:16

score 83 · Answer 4 · 2020-05-28 19:23:54

83

Views

Why does the integral $\int_{-\infty}^ \infty \frac{1}{x^2}dx$ diverge?

Published on 28 May 2020 - 19:23

score 329 · Answer 5 · 2020-05-28 19:57:15

329

Views

Find $\int_{0}^{\infty} \frac{\log(x) }{\sqrt{x} (x+1)^{2}}\,dx$

Published on 28 May 2020 - 19:57

score 24 · Answer 6 · 2020-05-28 21:04:31

24

Views

Integral solving with complex analysis

Published on 28 May 2020 - 21:04

score 105 · Answer 7 · 2026-03-30 03:56:47

105

Views

How to show $\int_0^\infty \cos\left(-1+\frac{ix}{\omega}\right)e^{-x}dx $ converges with epsilon-delta proof?

Published on 30 Mar 2026 - 3:56

score 143 · Answer 8 · 2020-05-29 22:23:22

143

Views

Finding the asymptotic of an integral

Published on 29 May 2020 - 22:23

score 65 · Answer 9 · 2020-05-30 03:42:37

65

Views

The equivalent condition for improper integral converges.

Published on 30 May 2020 - 3:42

score 106 · Answer 10 · 2020-05-30 04:18:58

106

Views

The product of improper Riemann integrable function and a bounded continuous function

Published on 30 May 2020 - 4:18

score 33 · Answer 11 · 2020-05-30 05:42:43

33

Views

Convergence of $\int_0^1\frac{1}{t^{\beta}}\sin(\frac{\pi}{t})dt$

Published on 30 May 2020 - 5:42

score 82 · Answer 12 · 2020-05-30 06:55:52

82

Views

Convergence $\int_0^{\pi/2}\frac{e^{\alpha \cos x}-\sqrt{1+2\cos x}}{\sqrt{\cos^5x}}\mathrm{d}x$

Published on 30 May 2020 - 6:55

score 133 · Answer 13 · 2020-05-31 08:35:02

133

Views

Value of $ \int _0^{+\infty }\frac{1}{\left(1+x^2\right)\left(1+x^{\alpha }\right)}dx$ while $\alpha$ is constant

Published on 31 May 2020 - 8:35

score 70 · Answer 14 · 2020-05-31 18:15:03

70

Views

Proving the asymptotic of $\int_0^\infty\frac{\sin x}{x^{a+1}}\,dx$ for $a \to 0^+$ is $\pi/2$

Published on 31 May 2020 - 18:15

score 352 · Answer 15 · 2020-06-01 03:02:27

352

Views

Show that $\int\limits_{-\infty}^\infty e^{-\pi x^2}dx = 1$

Published on 01 Jun 2020 - 3:02

List Question

How to compute $\parallel f \parallel_{L_2(\mathbb{R}^2)}$ for $f(x,y)=\frac{1}{1+(x-y)^2}$?

Evaluate a real integral, e.g. $\int_{0}^{\infty}\frac{x^2}{(x^2+1)(x^2+4)}\:\mathrm dx$ with complex analysis

Calculating $\Gamma (n+5/2)$

Why does the integral $\int_{-\infty}^ \infty \frac{1}{x^2}dx$ diverge?

Find $\int_{0}^{\infty} \frac{\log(x) }{\sqrt{x} (x+1)^{2}}\,dx$

Integral solving with complex analysis

How to show $\int_0^\infty \cos\left(-1+\frac{ix}{\omega}\right)e^{-x}dx $ converges with epsilon-delta proof?

Finding the asymptotic of an integral

The equivalent condition for improper integral converges.

The product of improper Riemann integrable function and a bounded continuous function

Convergence of $\int_0^1\frac{1}{t^{\beta}}\sin(\frac{\pi}{t})dt$

Convergence $\int_0^{\pi/2}\frac{e^{\alpha \cos x}-\sqrt{1+2\cos x}}{\sqrt{\cos^5x}}\mathrm{d}x$

Value of $ \int _0^{+\infty }\frac{1}{\left(1+x^2\right)\left(1+x^{\alpha }\right)}dx$ while $\alpha$ is constant

Proving the asymptotic of $\int_0^\infty\frac{\sin x}{x^{a+1}}\,dx$ for $a \to 0^+$ is $\pi/2$

Show that $\int\limits_{-\infty}^\infty e^{-\pi x^2}dx = 1$

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