Question

Evaluate $\int _0^{2\pi }\frac{\cos (n\theta) }{a+\cos\theta}\,d\theta$ with $a>1$, $n\in \mathbb{N}-\left\{0\right\}$

score 212 · Answer 1 · 2019-04-27 16:04:53

212

Views

Evaluate $\int _0^{2\pi }\frac{\cos (n\theta) }{a+\cos\theta}\,d\theta$ with $a>1$, $n\in \mathbb{N}-\left\{0\right\}$

Published on 27 Apr 2019 - 16:04

score 99 · Answer 2 · 2026-03-27 20:21:31

99

Views

Evaluate $\int _{-\infty }^{+\infty }\frac{\left(x-1\right)\cos(2x)}{x^2-4x+5}\,dx$

Published on 27 Mar 2026 - 20:21

score 394 · Answer 3 · 2026-03-25 07:49:14

394

Views

$\int_{-\infty}^\infty \frac{e^{pz}}{e^z-1}dz$ Cauchy principal value

Published on 25 Mar 2026 - 7:49

score 70 · Answer 4 · 2019-05-02 21:04:09

70

Views

Construct $\varphi (z)$ such that $\int_{|z|=1} \frac{\varphi (z)}{z-w} dz =0$

Published on 02 May 2019 - 21:04

score 159 · Answer 5 · 2019-05-03 16:32:20

159

Views

Integrating $\int_0^{\infty} \frac{\log x}{(x + a)^2 + b^2} \operatorname d\!x$

Published on 03 May 2019 - 16:32

score 307 · Answer 6 · 2026-03-24 22:01:39

307

Views

$\int_{0}^{\infty} \ln{(1+a x)}{x^{-b-1}} dx$ difficult integral with two branch cuts

Published on 24 Mar 2026 - 22:01

score 68 · Answer 7 · 2026-03-27 00:05:07

68

Views

Computing $\int_{|z-i|=\frac{3}{2}}\frac{e^{\frac{1}{z^2}}}{z^2+1}$

Published on 27 Mar 2026 - 0:05

score 861 · Answer 8 · 2026-03-27 20:24:42

861

Views

Finding the infinite sum involving $\coth$ function using contour integration

Published on 27 Mar 2026 - 20:24

score 37 · Answer 9 · 2026-03-25 07:40:24

37

Views

Analytic continuation and complex integration of one variable of a multivariate function

Published on 25 Mar 2026 - 7:40

score 156 · Answer 10 · 2026-03-25 14:38:00

156

Views

Formulations of Cauchy's theorem that don't seem consistent

Published on 25 Mar 2026 - 14:38

score 32 · Answer 11 · 2019-05-09 18:48:06

32

Views

Help with complex valued integral

Published on 09 May 2019 - 18:48

score 62 · Answer 12 · 2019-05-12 05:45:10

62

Views

contour integration - Estimation Lemma

Published on 12 May 2019 - 5:45

score 518 · Answer 13 · 2026-03-29 03:02:35

518

Views

Inverse Laplace transform of $\frac{π\cosh(\sqrt s)}{2 s^{3/2} \sinh(\sqrt s)}$ using complex integration

Published on 29 Mar 2026 - 3:02

score 335 · Answer 14 · 2026-03-27 23:37:53

335

Views

contour integration $\int_C \frac{\ln^2 z}{\sqrt{z}(1+z^2)}$(1 Short answer)

Published on 27 Mar 2026 - 23:37

score 55 · Answer 15 · 2019-05-16 13:39:46

55

Views

Calculating $\oint_{\gamma}\bar z^ndz$ for a known path

Published on 16 May 2019 - 13:39

List Question

Evaluate $\int _0^{2\pi }\frac{\cos (n\theta) }{a+\cos\theta}\,d\theta$ with $a>1$, $n\in \mathbb{N}-\left\{0\right\}$

Evaluate $\int _{-\infty }^{+\infty }\frac{\left(x-1\right)\cos(2x)}{x^2-4x+5}\,dx$

$\int_{-\infty}^\infty \frac{e^{pz}}{e^z-1}dz$ Cauchy principal value

Construct $\varphi (z)$ such that $\int_{|z|=1} \frac{\varphi (z)}{z-w} dz =0$

Integrating $\int_0^{\infty} \frac{\log x}{(x + a)^2 + b^2} \operatorname d\!x$

$\int_{0}^{\infty} \ln{(1+a x)}{x^{-b-1}} dx$ difficult integral with two branch cuts

Computing $\int_{|z-i|=\frac{3}{2}}\frac{e^{\frac{1}{z^2}}}{z^2+1}$

Finding the infinite sum involving $\coth$ function using contour integration

Analytic continuation and complex integration of one variable of a multivariate function

Formulations of Cauchy's theorem that don't seem consistent

Help with complex valued integral

contour integration - Estimation Lemma

Inverse Laplace transform of $\frac{π\cosh(\sqrt s)}{2 s^{3/2} \sinh(\sqrt s)}$ using complex integration

contour integration $\int_C \frac{\ln^2 z}{\sqrt{z}(1+z^2)}$(1 Short answer)

Calculating $\oint_{\gamma}\bar z^ndz$ for a known path

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