List questions from residue-calculus

Published on 02 Apr 2019 - 21:41

46

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Compute $\oint\frac{e^{2z}+\sin z}{(z^2+1)^3}dz$, over the curve C

Published on 04 Apr 2019 - 15:05

83

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Find $\oint\exp((z-1)^{-1})(z+3)^{-1}\,dz$

Published on 26 Mar 2026 - 18:41

482

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Show $\frac{f(z)}{\sin(\pi z)} = \sum_{-\infty}^{\infty} \frac{(-1)^nf(n)}{(z-n)}$

Published on 25 Mar 2026 - 17:20

270

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Integral $\oint_{\gamma}\frac {\cos z}{z}dz$ on 2 curves

Published on 27 Mar 2026 - 12:07

81

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$\oint_{\gamma}\frac 1{z^2+1}dz$ on different curves

Published on 27 Mar 2026 - 12:08

125

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Closed-form expression for residue of a pole of order 2

Published on 07 Apr 2019 - 7:57

166

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Calculate $\oint_{\gamma}\frac {\sin z}{z(z-2i)}dz$ on $|z| =3$ in trigonometric sense and on the inverse trigonometric sense.

Published on 27 Mar 2026 - 12:03

132

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Compute $\oint_{\gamma}f(z)dz$, where $f(z)=\frac {ze^{\pi z}}{z^4-16}+ze^{\frac \pi z}$ where $\gamma:9x^2+y^2=9$

Published on 27 Mar 2026 - 12:03

29

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Res($\zeta(s+2) \Gamma(s)\cos(\frac{\pi s}{2})x^{-s}$|$s=-1$)?

Published on 07 Apr 2019 - 14:50

200

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Computation of integral $\int_{\rho} \frac{dz}{(z-a)(z-b)}$

Published on 07 Apr 2019 - 19:29

31

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Residues of $\frac{e^{iwx}}{kw^2+s}$

Published on 10 Apr 2019 - 8:05

57

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Finding $\mathcal{L}^{-1}_t\left(\frac{e^{|x|\sqrt{\frac{s}{k}}}}{\sqrt{ks}}\right)$ Using the General Inversion Formula

Published on 11 Apr 2019 - 0:20

78

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Calculus of Residue

Published on 27 Mar 2026 - 13:46

87

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Integral through complex methods $\int_{0}^{2\pi}\log \sin^{2}2\theta d\theta=4\int_{0}^{\pi}\log \sin\theta d\theta=-4\pi \log 2$

Published on 13 Apr 2019 - 23:20

List Question

Residue theorem /Integral

Compute $\oint\frac{e^{2z}+\sin z}{(z^2+1)^3}dz$, over the curve C

Find $\oint\exp((z-1)^{-1})(z+3)^{-1}\,dz$

Show $\frac{f(z)}{\sin(\pi z)} = \sum_{-\infty}^{\infty} \frac{(-1)^nf(n)}{(z-n)}$

Integral $\oint_{\gamma}\frac {\cos z}{z}dz$ on 2 curves

$\oint_{\gamma}\frac 1{z^2+1}dz$ on different curves

Closed-form expression for residue of a pole of order 2

Calculate $\oint_{\gamma}\frac {\sin z}{z(z-2i)}dz$ on $|z| =3$ in trigonometric sense and on the inverse trigonometric sense.

Compute $\oint_{\gamma}f(z)dz$, where $f(z)=\frac {ze^{\pi z}}{z^4-16}+ze^{\frac \pi z}$ where $\gamma:9x^2+y^2=9$

Res($\zeta(s+2) \Gamma(s)\cos(\frac{\pi s}{2})x^{-s}$|$s=-1$)?

Computation of integral $\int_{\rho} \frac{dz}{(z-a)(z-b)}$

Residues of $\frac{e^{iwx}}{kw^2+s}$

Finding $\mathcal{L}^{-1}_t\left(\frac{e^{|x|\sqrt{\frac{s}{k}}}}{\sqrt{ks}}\right)$ Using the General Inversion Formula

Calculus of Residue

Integral through complex methods $\int_{0}^{2\pi}\log \sin^{2}2\theta d\theta=4\int_{0}^{\pi}\log \sin\theta d\theta=-4\pi \log 2$

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