List questions from residue-calculus

Published on 26 Mar 2026 - 17:13

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Integrate $\int_0^{2\pi} \frac{(\cos^2{x})^{2-\beta}}{(1+\alpha \cos{x})^{4-\beta}} dx$

Published on 29 May 2020 - 19:58

60

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Finding residues of $\frac{z}{e^z+e^{-z}}$.

Published on 29 May 2020 - 21:56

95

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Residue at essential singularity of $\frac{\mathrm{e}^{\frac{1}{z}}}{z^2-2z+2}$

Published on 31 May 2020 - 6:03

65

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How to deal with a singularity on the integration contour

Published on 02 Jun 2020 - 14:44

40

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Show that $ \int_{-\infty}^{\infty} \frac{x}{x^4+1} e^{-ikx}dx=- \pi ie^{-k/ \sqrt{2}}\sin(k/ \sqrt{2}) $ for $k>0$

Published on 02 Jun 2020 - 16:55

59

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Compute the complex

Published on 26 Mar 2026 - 17:11

132

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Finding the poles of a certain Zeta function

Published on 26 Mar 2026 - 4:30

75

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Calculating of sum $\sum_{z:\:z^n = 1} \frac{1}{2+z}$ with residues

Published on 27 Mar 2026 - 21:05

320

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Integrate $\int_0^{2\pi}\frac{\ln(a + b\cos x)}{c + d\cos x} dx$, Residue theorem

Published on 07 Jun 2020 - 20:38

82

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Calcuating an Integral via Residues

Published on 08 Jun 2020 - 4:08

551

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Why are the integrals over $\cos(z)$ and $e^{iz}$ so closely related

Published on 09 Jun 2020 - 14:03

106

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

Published on 10 Jun 2020 - 15:54

903

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Value of the contour integral around an essential singularity of $1/(e^z-1) \cdot 1/(e^{1/z}-1)$.

Published on 25 Mar 2026 - 12:50

79

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The residue calculus

Published on 10 Jun 2020 - 20:45

List Question

Contradiction of Cauchy's Residue theorem?

Integrate $\int_0^{2\pi} \frac{(\cos^2{x})^{2-\beta}}{(1+\alpha \cos{x})^{4-\beta}} dx$

Finding residues of $\frac{z}{e^z+e^{-z}}$.

Residue at essential singularity of $\frac{\mathrm{e}^{\frac{1}{z}}}{z^2-2z+2}$

How to deal with a singularity on the integration contour

Show that $ \int_{-\infty}^{\infty} \frac{x}{x^4+1} e^{-ikx}dx=- \pi ie^{-k/ \sqrt{2}}\sin(k/ \sqrt{2}) $ for $k>0$

Compute the complex

Finding the poles of a certain Zeta function

Calculating of sum $\sum_{z:\:z^n = 1} \frac{1}{2+z}$ with residues

Integrate $\int_0^{2\pi}\frac{\ln(a + b\cos x)}{c + d\cos x} dx$, Residue theorem

Calcuating an Integral via Residues

Why are the integrals over $\cos(z)$ and $e^{iz}$ so closely related

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

Value of the contour integral around an essential singularity of $1/(e^z-1) \cdot 1/(e^{1/z}-1)$.

The residue calculus

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