List questions from residue-calculus

Published on 25 Mar 2026 - 13:05

68

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How do I evaluate the integral $\frac{-i}{2(2\pi)^2r}\int_{-\infty}^{\infty}dp\frac{p\exp(ipr)}{\sqrt{p^2+m^2}}$?

Published on 06 Feb 2018 - 15:57

121

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Evaluate $ \int_0^\infty x^{a-1}\frac{\sin(\frac{1}{2}a \pi-bx)}{x^2+r^2}\, r\,dx $

Published on 23 Mar 2026 - 21:06

622

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Residue of composite functions

Published on 23 Mar 2026 - 10:38

761

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Trigonometric integral with square root (residue theorem)

Published on 25 Mar 2026 - 6:19

473

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Laurent series and radius of convergence of $f(z)=\frac{1}{(1-\cosh z)^2}$

Published on 25 Mar 2026 - 18:29

69

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Complex integration with residues $\int_0^{2\pi}\frac{d\phi}{(p+q\cos\phi)^2}=\frac{2\pi p}{(p^2-q^2)^{3/2}}$

Published on 11 Feb 2018 - 20:09

1.3k

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how to calculate the value of $\int_{-\infty}^\infty \frac{e^{ax}}{\cosh x}\,dx$

Published on 19 Mar 2026 - 22:02

97

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definite integration of a trigonometric function with branch cut

Published on 19 Mar 2026 - 23:51

73

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Calculate $\int_{\gamma} \frac{z^2}{\sin(z^3)} dz $ where $\gamma=\{z \in \mathbb{C} : |z|=\frac{3}{2}\}$

Published on 20 Mar 2026 - 8:28

97

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Laplace inverse, using inversion formula

Published on 25 Mar 2026 - 6:17

44

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Help using contour integration/any other method?

Published on 25 Mar 2026 - 7:40

96

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Question about poles and zeros of a general $f(z)$

Published on 17 Mar 2026 - 7:16

2.2k

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Find the residue of $\frac{z^2}{(z-1)(z-2)(z-3)}$ at $\infty$.

Published on 24 Mar 2026 - 20:46

244

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Compute the given integral using the residue theorem

Published on 17 Mar 2026 - 12:28

List Question

Laurent Series problems

How do I evaluate the integral $\frac{-i}{2(2\pi)^2r}\int_{-\infty}^{\infty}dp\frac{p\exp(ipr)}{\sqrt{p^2+m^2}}$?

Evaluate $ \int_0^\infty x^{a-1}\frac{\sin(\frac{1}{2}a \pi-bx)}{x^2+r^2}\, r\,dx $

Residue of composite functions

Trigonometric integral with square root (residue theorem)

Laurent series and radius of convergence of $f(z)=\frac{1}{(1-\cosh z)^2}$

Complex integration with residues $\int_0^{2\pi}\frac{d\phi}{(p+q\cos\phi)^2}=\frac{2\pi p}{(p^2-q^2)^{3/2}}$

how to calculate the value of $\int_{-\infty}^\infty \frac{e^{ax}}{\cosh x}\,dx$

definite integration of a trigonometric function with branch cut

Calculate $\int_{\gamma} \frac{z^2}{\sin(z^3)} dz $ where $\gamma=\{z \in \mathbb{C} : |z|=\frac{3}{2}\}$

Laplace inverse, using inversion formula

Help using contour integration/any other method?

Question about poles and zeros of a general $f(z)$

Find the residue of $\frac{z^2}{(z-1)(z-2)(z-3)}$ at $\infty$.

Compute the given integral using the residue theorem

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