List questions from contour-integration

Published on 01 Apr 2026 - 19:44

156

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Contour integral $\int_0^{2\pi}e^{-\cos\theta} \cos⁡(n\theta+\sin\theta)~d\theta$

Published on 28 May 2023 - 7:44

166

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Barnes beta - like integral mistake

Published on 28 May 2023 - 8:38

50

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Uniqueness of a Contour Integral

Published on 30 Mar 2026 - 0:19

240

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Evaluating $\int_{-\infty}^{+\infty}\frac{\sin{(\cosh{x})}\cosh{x}}{1+\cosh^{2}{x}}dx$

Published on 27 Mar 2026 - 14:51

132

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Why only one singularity is involved? $\int_{0}^{2\pi} \frac{1}{13+5\sin(\theta)}~d\theta$

Published on 27 Mar 2026 - 13:25

445

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Deriving the characteristic function of the Cauchy distribution by residue theorem

Published on 01 Jun 2023 - 16:32

123

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Compute residues for $\int_{-\infty}^{\infty} \frac{x \sin x}{1+x^4}dx$

Published on 01 Jun 2023 - 17:03

123

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Riemann Hypothesis Research

Published on 26 Mar 2026 - 4:28

64

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Integral related to binomial coefficient $\frac{1}{2\pi}\int_{-\pi}^{\pi}\frac{(1+e^{ix})^n}{e^{ixk}}~dx$

Published on 02 Jun 2023 - 17:39

97

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Residues at Infinity $\oint_C \frac{\sin ^2 z}{z^2(z-1)}dz$

Published on 30 Mar 2026 - 0:21

238

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Evaluate $\int_{0}^{1} \frac{(1+5x^2)\arctan(x)^2}{x^{5/4}(1-x^2)^{1/4}} \text{d}x$

Published on 04 Jun 2023 - 5:17

114

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Where is the contradiction? $I=\int_0^\infty \frac{a^x}{x^2+1}dx,~~0<a<1$

Published on 04 Jun 2023 - 5:19

315

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Compute the integral $\int_{0}^{\pi/2} \cos^a (x) \sin (a x) \ dx$

Published on 06 Jun 2023 - 7:04

76

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Analysing an integral asymptotically

Published on 25 Mar 2026 - 17:23

List Question

How should I show that this integral is 0?

Contour integral $\int_0^{2\pi}e^{-\cos\theta} \cos⁡(n\theta+\sin\theta)~d\theta$

Barnes beta - like integral mistake

Uniqueness of a Contour Integral

Evaluating $\int_{-\infty}^{+\infty}\frac{\sin{(\cosh{x})}\cosh{x}}{1+\cosh^{2}{x}}dx$

Why only one singularity is involved? $\int_{0}^{2\pi} \frac{1}{13+5\sin(\theta)}~d\theta$

Deriving the characteristic function of the Cauchy distribution by residue theorem

Compute residues for $\int_{-\infty}^{\infty} \frac{x \sin x}{1+x^4}dx$

Riemann Hypothesis Research

Integral related to binomial coefficient $\frac{1}{2\pi}\int_{-\pi}^{\pi}\frac{(1+e^{ix})^n}{e^{ixk}}~dx$

Residues at Infinity $\oint_C \frac{\sin ^2 z}{z^2(z-1)}dz$

Evaluate $\int_{0}^{1} \frac{(1+5x^2)\arctan(x)^2}{x^{5/4}(1-x^2)^{1/4}} \text{d}x$

Where is the contradiction? $I=\int_0^\infty \frac{a^x}{x^2+1}dx,~~0<a<1$

Compute the integral $\int_{0}^{\pi/2} \cos^a (x) \sin (a x) \ dx$

Analysing an integral asymptotically

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