Question

Can Cauchy's Theorem be used to solve a contour integral with singularities?

score 210 · Answer 1 · 2026-03-27 13:27:20

210

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Can Cauchy's Theorem be used to solve a contour integral with singularities?

Published on 27 Mar 2026 - 13:27

score 111 · Answer 2 · 2026-04-05 04:34:32

111

Views

Infinite integral of $e^{-\alpha t^\beta} \cos(\omega t)$

Published on 05 Apr 2026 - 4:34

score 39 · Answer 3 · 2023-10-21 14:18:14

39

Views

Winding number of composition equaling zero implies existence of complex logarithm

Published on 21 Oct 2023 - 14:18

score 138 · Answer 4 · 2026-03-25 16:03:46

138

Views

Asymptotic expansion of an inverse Fourier integral

Published on 25 Mar 2026 - 16:03

score 42 · Answer 5 · 2026-03-25 18:47:20

42

Views

Mellin-Barnes integrals as "master integrals" in code for automated computation of Feynman graphs

Published on 25 Mar 2026 - 18:47

score 71 · Answer 6 · 2023-11-04 23:59:59

71

Views

Contour integration of $\frac{\sinh(az)}{\sinh(\pi z)} $

Published on 04 Nov 2023 - 23:59

score 149 · Answer 7 · 2023-11-06 22:41:46

149

Views

Contour integration of $ \int_{-1}^{1} \frac{dz}{\sqrt{1-z^2}(a+bz)}$

Published on 06 Nov 2023 - 22:41

score 43 · Answer 8 · 2023-11-07 22:16:14

43

Views

Residue Theorem for infinite oscillation

Published on 07 Nov 2023 - 22:16

score 28 · Answer 9 · 2026-03-26 02:35:55

28

Views

Substitutions for integrals involving branch cuts

Published on 26 Mar 2026 - 2:35

score 81 · Answer 10 · 2023-11-24 01:42:33

81

Views

Show the identity $\frac{\pi^2}{\sin^2(a\pi)}=\sum_{n=-\infty}^{\infty}\frac{1}{(a+n)^2}$ using complex analysis

Published on 24 Nov 2023 - 1:42

score 62 · Answer 11 · 2023-11-24 04:51:52

62

Views

Complex variable solution for integral involving $\frac{\sin^{2}v}{a+b\cos v} $

Published on 24 Nov 2023 - 4:51

score 69 · Answer 12 · 2023-11-25 06:44:18

69

Views

Evaluate $\int_{-\infty}^{\infty} \frac{\log(x+i)}{x^2+1} \text{d}x$

Published on 25 Nov 2023 - 6:44

score 68 · Answer 13 · 2023-11-28 01:27:43

68

Views

Clarification on the Parametrizations of a Keyhole Contour

Published on 28 Nov 2023 - 1:27

score 71 · Answer 14 · 2023-11-29 05:16:34

71

Views

Calculate an integration on a sphere

Published on 29 Nov 2023 - 5:16

score 109 · Answer 15 · 2026-03-25 19:07:21

109

Views

Show that $\frac{1}{2\pi i}\int_{\gamma_p}z\frac{h'(z)}{h(z)}dz$ is in $\mathbb{Z}+\mathbb{Z}\tau$

Published on 25 Mar 2026 - 19:07

List Question

Can Cauchy's Theorem be used to solve a contour integral with singularities?

Infinite integral of $e^{-\alpha t^\beta} \cos(\omega t)$

Winding number of composition equaling zero implies existence of complex logarithm

Asymptotic expansion of an inverse Fourier integral

Mellin-Barnes integrals as "master integrals" in code for automated computation of Feynman graphs

Contour integration of $\frac{\sinh(az)}{\sinh(\pi z)} $

Contour integration of $ \int_{-1}^{1} \frac{dz}{\sqrt{1-z^2}(a+bz)}$

Residue Theorem for infinite oscillation

Substitutions for integrals involving branch cuts

Show the identity $\frac{\pi^2}{\sin^2(a\pi)}=\sum_{n=-\infty}^{\infty}\frac{1}{(a+n)^2}$ using complex analysis

Complex variable solution for integral involving $\frac{\sin^{2}v}{a+b\cos v} $

Evaluate $\int_{-\infty}^{\infty} \frac{\log(x+i)}{x^2+1} \text{d}x$

Clarification on the Parametrizations of a Keyhole Contour

Calculate an integration on a sphere

Show that $\frac{1}{2\pi i}\int_{\gamma_p}z\frac{h'(z)}{h(z)}dz$ is in $\mathbb{Z}+\mathbb{Z}\tau$

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