Question

Show that $\frac{1}{2\pi} \int_0^{2\pi} e^{ik\theta}d\theta = 1$ or $0$ depending on $k$.

score 133 · Answer 1 · 2014-10-15 03:28:02

133

Views

Show that $\frac{1}{2\pi} \int_0^{2\pi} e^{ik\theta}d\theta = 1$ or $0$ depending on $k$.

Published on 15 Oct 2014 - 3:28

score 1.2k · Answer 2 · 2014-10-15 21:15:12

1.2k

Views

Compute $\int_{\gamma} \frac{z}{z^3-1} dz$ where $\gamma$ is circle centered at origin of radius 2

Published on 15 Oct 2014 - 21:15

score 1.6k · Answer 3 · 2026-03-27 07:57:18

1.6k

Views

Half-Fourier transform, relation to Delta function

Published on 27 Mar 2026 - 7:57

score 385 · Answer 4 · 2014-10-22 14:43:20

385

Views

Fourier series representation of $\sin^4 x$

Published on 22 Oct 2014 - 14:43

score 81 · Answer 5 · 2014-10-23 00:51:10

81

Views

Complex Integration and deduce that function is constant

Published on 23 Oct 2014 - 0:51

score 471 · Answer 6 · 2014-10-25 01:09:46

471

Views

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Published on 25 Oct 2014 - 1:09

score 91 · Answer 7 · 2014-10-27 03:37:48

91

Views

Show that $\int_{|z|=1} \frac{e^z}{z^k} dz = \frac{2\pi i}{(k-1)!}$

Published on 27 Oct 2014 - 3:37

score 305 · Answer 8 · 2014-10-31 08:40:51

305

Views

Sum of Lomax random variables

Published on 31 Oct 2014 - 8:40

score 131 · Answer 9 · 2014-11-01 11:51:09

131

Views

How to integrate $\int_{-1}^1\frac{1}{a + bx }dx$, where $a,b\in \mathbb{C}$ without using branch cuts.

Published on 01 Nov 2014 - 11:51

score 115 · Answer 10 · 2014-11-02 05:05:53

115

Views

$\int_{\gamma}^{}\frac{1}{z}dz$, $\gamma$ is the ellipse $x^2+4y^2=1$ traversed once with the positive orientation

Published on 02 Nov 2014 - 5:05

score 5.7k · Answer 11 · 2014-11-02 05:59:32

5.7k

Views

Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$

Published on 02 Nov 2014 - 5:59

score 425 · Answer 12 · 2014-11-02 10:09:57

425

Views

Homework: Complex integral equation

Published on 02 Nov 2014 - 10:09

score 341 · Answer 13 · 2014-11-02 13:07:56

341

Views

If f is analytic in the unit disk and $|f(z)|\leq \frac{1}{1-|z|}$ then $|f'(0)|\leq 4$

Published on 02 Nov 2014 - 13:07

score 338 · Answer 14 · 2014-11-04 00:43:06

338

Views

Poisson Integral is equal to 1

Published on 04 Nov 2014 - 0:43

score 220 · Answer 15 · 2014-11-06 02:39:19

220

Views

Evaluate $\int_{|z|=r}^{}\frac{\log\ z}{z^2+1}dz$ where $r>0$

Published on 06 Nov 2014 - 2:39

List Question

Show that $\frac{1}{2\pi} \int_0^{2\pi} e^{ik\theta}d\theta = 1$ or $0$ depending on $k$.

Compute $\int_{\gamma} \frac{z}{z^3-1} dz$ where $\gamma$ is circle centered at origin of radius 2

Half-Fourier transform, relation to Delta function

Fourier series representation of $\sin^4 x$

Complex Integration and deduce that function is constant

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Show that $\int_{|z|=1} \frac{e^z}{z^k} dz = \frac{2\pi i}{(k-1)!}$

Sum of Lomax random variables

How to integrate $\int_{-1}^1\frac{1}{a + bx }dx$, where $a,b\in \mathbb{C}$ without using branch cuts.

$\int_{\gamma}^{}\frac{1}{z}dz$, $\gamma$ is the ellipse $x^2+4y^2=1$ traversed once with the positive orientation

Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$

Homework: Complex integral equation

If f is analytic in the unit disk and $|f(z)|\leq \frac{1}{1-|z|}$ then $|f'(0)|\leq 4$

Poisson Integral is equal to 1

Evaluate $\int_{|z|=r}^{}\frac{\log\ z}{z^2+1}dz$ where $r>0$

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