List questions from residue-calculus

Published on 02 May 2026 - 18:48

127

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Is the solution to this integral correct

Published on 11 Apr 2026 - 23:17

476

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Residue of $\sin(\tan(z))$ at $z=\frac{\pi}{2}$

Published on 13 Apr 2026 - 20:26

505

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Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Published on 16 Apr 2026 - 2:50

5.3k

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Integrate sin(nx)sin(mx) from 0 to 2$\pi$ using residuals

Published on 16 Apr 2026 - 15:06

792

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Evaluate $\int_0^\infty \frac{x^2}{x^4 + 6x^2 + 13}dx$

Published on 17 Apr 2026 - 8:06

136

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Evaluate the integral $\int_0^1 \frac{x^n}{x^a(1-x)^{1-a}}\mathrm{d}x$ for any integer $n$.

Published on 17 Apr 2026 - 13:48

135

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Evaluating integral with residues

Published on 10 Apr 2026 - 23:04

152

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Upper bound for residue of a rational function with zeros and poles in the disk

Published on 29 Apr 2026 - 12:27

140

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Finding the poles of a complex function in order to find the complex integral $\int_C \frac{dz}{1+z^n}$ using residues?

Published on 11 Apr 2026 - 22:41

67

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Contour Complex integral using Residue

Published on 10 Apr 2026 - 21:12

304

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Does the residue always exist for an isolated singularity?

Published on 14 Apr 2026 - 2:08

132

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Residue Theorem and Improper Integral

Published on 14 Apr 2026 - 11:21

105

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How to prove $\int_{-\infty}^\infty dx \frac{e^{ixz}}{x-i\epsilon} = 2\pi i \Theta(z)$

Published on 15 Apr 2026 - 21:46

87

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Inconsistency of DCT and Residue theorem

Published on 13 Apr 2026 - 19:05

List Question

Integral on semicircular arc of a function with a simple pole at $z=0$

Is the solution to this integral correct

Residue of $\sin(\tan(z))$ at $z=\frac{\pi}{2}$

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Integrate sin(nx)sin(mx) from 0 to 2$\pi$ using residuals

Evaluate $\int_0^\infty \frac{x^2}{x^4 + 6x^2 + 13}dx$

Evaluate the integral $\int_0^1 \frac{x^n}{x^a(1-x)^{1-a}}\mathrm{d}x$ for any integer $n$.

Evaluating integral with residues

Upper bound for residue of a rational function with zeros and poles in the disk

Finding the poles of a complex function in order to find the complex integral $\int_C \frac{dz}{1+z^n}$ using residues?

Contour Complex integral using Residue

Does the residue always exist for an isolated singularity?

Residue Theorem and Improper Integral

How to prove $\int_{-\infty}^\infty dx \frac{e^{ixz}}{x-i\epsilon} = 2\pi i \Theta(z)$

Inconsistency of DCT and Residue theorem

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