Question

Why is $\cos \pi x$ needed in $\sum\limits_{n=-\infty}^\infty g(n)=\frac1{2i}\oint_{|x|=\infty}\frac{\cos \pi x}{\sin \pi x}g(x)\,\mathrm dx$?

score 111 · Answer 1 · 2018-12-06 02:30:04

111

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Why is $\cos \pi x$ needed in $\sum\limits_{n=-\infty}^\infty g(n)=\frac1{2i}\oint_{|x|=\infty}\frac{\cos \pi x}{\sin \pi x}g(x)\,\mathrm dx$?

Published on 06 Dec 2018 - 2:30

score 197 · Answer 2 · 2026-03-28 05:23:27

197

Views

Integral $\int_{0}^{\infty}\frac{1}{x^2}(\frac{1}{\cosh^2x}-\frac{\tanh{x}}{x})dx$

Published on 28 Mar 2026 - 5:23

score 1.7k · Answer 3 · 2026-03-26 12:05:52

1.7k

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Using the residue theorem to evaluate an integral

Published on 26 Mar 2026 - 12:05

score 442 · Answer 4 · 2026-03-25 00:07:47

442

Views

Evaluate $\int_{-\infty}^\infty \frac{1}{\sqrt{z^2 + 1}}\frac{1}{z - \alpha} dz$.

Published on 25 Mar 2026 - 0:07

score 65 · Answer 5 · 2026-03-27 14:55:26

65

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how to integrate $\frac{-1+e^{-i k x}}{x^2}$

Published on 27 Mar 2026 - 14:55

score 93 · Answer 6 · 2018-12-11 23:57:28

93

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contour integral with given contour

Published on 11 Dec 2018 - 23:57

score 97 · Answer 7 · 2026-03-27 10:38:06

97

Views

Is the residue theorem the correct approach for this integral?

Published on 27 Mar 2026 - 10:38

score 2.1k · Answer 8 · 2026-03-25 07:39:47

2.1k

Views

Cauchy Principal Value calculation

Published on 25 Mar 2026 - 7:39

score 105 · Answer 9 · 2018-12-13 00:45:46

105

Views

Stuck on contour integral, can I use Cauchy's theorem instead?

Published on 13 Dec 2018 - 0:45

score 113 · Answer 10 · 2026-03-28 06:18:02

113

Views

How to integrate $\int_0^{+\infty} \frac{x^2\ln x}{x^4-x^3+1}\,\mathrm{d}x$?

Published on 28 Mar 2026 - 6:18

score 209 · Answer 11 · 2026-03-25 16:20:29

209

Views

Stuck on proof using Cauchy's integral formula

Published on 25 Mar 2026 - 16:20

score 92 · Answer 12 · 2018-12-13 10:31:23

92

Views

Use The Fundamental Theorem of Contour Integration or otherwise to evaluate the following integrals. (If it can't be used state why)

Published on 13 Dec 2018 - 10:31

score 149 · Answer 13 · 2026-03-29 20:20:51

149

Views

Showing that the limit of contour integrals is zero

Published on 29 Mar 2026 - 20:20

score 137 · Answer 14 · 2026-03-28 03:27:28

137

Views

Closed from of $\int_0^{\infty} \frac{e^{iax}}{x^{n}+1}dx$?

Published on 28 Mar 2026 - 3:27

score 259 · Answer 15 · 2018-12-14 20:23:40

259

Views

Contour integral over a non-rectifiable contour

Published on 14 Dec 2018 - 20:23

List Question

Why is $\cos \pi x$ needed in $\sum\limits_{n=-\infty}^\infty g(n)=\frac1{2i}\oint_{|x|=\infty}\frac{\cos \pi x}{\sin \pi x}g(x)\,\mathrm dx$?

Integral $\int_{0}^{\infty}\frac{1}{x^2}(\frac{1}{\cosh^2x}-\frac{\tanh{x}}{x})dx$

Using the residue theorem to evaluate an integral

Evaluate $\int_{-\infty}^\infty \frac{1}{\sqrt{z^2 + 1}}\frac{1}{z - \alpha} dz$.

how to integrate $\frac{-1+e^{-i k x}}{x^2}$

contour integral with given contour

Is the residue theorem the correct approach for this integral?

Cauchy Principal Value calculation

Stuck on contour integral, can I use Cauchy's theorem instead?

How to integrate $\int_0^{+\infty} \frac{x^2\ln x}{x^4-x^3+1}\,\mathrm{d}x$?

Stuck on proof using Cauchy's integral formula

Use The Fundamental Theorem of Contour Integration or otherwise to evaluate the following integrals. (If it can't be used state why)

Showing that the limit of contour integrals is zero

Closed from of $\int_0^{\infty} \frac{e^{iax}}{x^{n}+1}dx$?

Contour integral over a non-rectifiable contour

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