List questions from contour-integration

Published on 11 Apr 2026 - 15:22

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Show that $\int_0^{\pi}\frac {\cos {n \theta}}{1-2r\cos \theta+r^2}\, \mathrm d \theta = \frac {\pi r^n}{1-r^2}$

Published on 05 May 2016 - 12:34

46

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Compute an integral involving exterior Riemann mapping

Published on 11 Apr 2026 - 2:10

144

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Evaluate $I(x)=\int_{-\infty}^{\infty}\frac{e^{xv}}{1+e^v}dv$

Published on 08 May 2016 - 2:59

71

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Show that $\displaystyle \int_{\gamma_R}\exp(-w^2)\,\mathrm dw\to 0~(R\to\infty)$ along $\gamma_R(t)=R\exp(\mathrm it)$

Published on 28 Mar 2026 - 11:34

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Evaluate $\int_0^{2\pi}\frac{\sin^2(x)}{a + b\cos(x)}\ dx$ using a suitable contour

Published on 08 May 2016 - 19:16

136

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$ f(z) = \int _{0} ^\infty e^{-z t^2} dt $ is holomorphic in $Re(z) > 0$

Published on 10 May 2016 - 20:18

193

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Showing that a function is the restriction of another holomorphic function

Published on 27 Mar 2026 - 1:44

130

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Evaluate the following contour integral

Published on 13 May 2016 - 12:09

88

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How to prove reflection positivity for $|x|^{-p}$ using Fourier transform (and contour integrals)

Published on 12 Apr 2026 - 4:24

215

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Choice of branch cut

Published on 12 Apr 2026 - 12:55

147

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Proof of the Primitive Existence Theorem

Published on 12 Apr 2026 - 12:27

873

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Complex Contour Integral Involving Arg(z)

Published on 13 Apr 2026 - 12:02

32

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Integral estimation

Published on 09 Apr 2026 - 15:00

178

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Integral of $p(x)\operatorname{csch}(x)$

Published on 13 Apr 2026 - 9:40

List Question

Double Integral with Residues

Show that $\int_0^{\pi}\frac {\cos {n \theta}}{1-2r\cos \theta+r^2}\, \mathrm d \theta = \frac {\pi r^n}{1-r^2}$

Compute an integral involving exterior Riemann mapping

Evaluate $I(x)=\int_{-\infty}^{\infty}\frac{e^{xv}}{1+e^v}dv$

Show that $\displaystyle \int_{\gamma_R}\exp(-w^2)\,\mathrm dw\to 0~(R\to\infty)$ along $\gamma_R(t)=R\exp(\mathrm it)$

Evaluate $\int_0^{2\pi}\frac{\sin^2(x)}{a + b\cos(x)}\ dx$ using a suitable contour

$ f(z) = \int _{0} ^\infty e^{-z t^2} dt $ is holomorphic in $Re(z) > 0$

Showing that a function is the restriction of another holomorphic function

Evaluate the following contour integral

How to prove reflection positivity for $|x|^{-p}$ using Fourier transform (and contour integrals)

Choice of branch cut

Proof of the Primitive Existence Theorem

Complex Contour Integral Involving Arg(z)

Integral estimation

Integral of $p(x)\operatorname{csch}(x)$

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