List questions from residue-calculus

Published on 25 Mar 2026 - 6:03

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Calculate $\int_0^1 \frac{1}{\sqrt{x(1-x)}} dx$ using residue calculus

Published on 07 Jan 2019 - 0:27

158

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Residue of $f(z)=\frac{z}{\sin{\left(\frac{\pi}{z+1}\right)}}$ in all isolated singularities

Published on 26 Mar 2026 - 13:45

61

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Solving integral using residues

Published on 07 Jan 2019 - 18:54

737

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Cauchy Principal Value and Residue Theorem: Apparent Contradiction

Published on 25 Mar 2026 - 7:42

150

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How to use complex analysis to evaluate the trigonometric integral $\int_{0}^{2 \pi}{\frac {\cos \left( x \right) }{2+\cos \left( x \right) }}$

Published on 27 Mar 2026 - 4:38

335

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Residue and Laurent Series, is this valid?

Published on 26 Mar 2026 - 15:17

425

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Residues of $\frac{\pi \cot(\pi z)}{(z+1)(z+2)}$

Published on 16 Jan 2019 - 0:08

66

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Connection between sums and integrals over closed paths and their areas

Published on 17 Jan 2019 - 15:14

1.8k

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Proof without words of $\oint zdz = 0$ and $\oint dz/z = 2\pi i$

Published on 25 Mar 2026 - 10:57

41

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Laurent series/isolated singularity

Published on 25 Mar 2026 - 11:08

137

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Estimating complex integral

Published on 27 Mar 2026 - 1:14

820

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Calculate the value of $\int_0^\infty \frac{\sqrt{x}\cos(\ln(x))}{x^2+1}\,dx$

Published on 25 Jan 2019 - 18:19

105

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How to calculate the arc part when using Residue theorem?

Published on 26 Jan 2019 - 22:41

3.8k

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Integral of real part of $z$ around the unit circle

Published on 25 Mar 2026 - 3:21

List Question

Shifting roots in infinite sums of polynomials

Calculate $\int_0^1 \frac{1}{\sqrt{x(1-x)}} dx$ using residue calculus

Residue of $f(z)=\frac{z}{\sin{\left(\frac{\pi}{z+1}\right)}}$ in all isolated singularities

Solving integral using residues

Cauchy Principal Value and Residue Theorem: Apparent Contradiction

How to use complex analysis to evaluate the trigonometric integral $\int_{0}^{2 \pi}{\frac {\cos \left( x \right) }{2+\cos \left( x \right) }}$

Residue and Laurent Series, is this valid?

Residues of $\frac{\pi \cot(\pi z)}{(z+1)(z+2)}$

Connection between sums and integrals over closed paths and their areas

Proof without words of $\oint zdz = 0$ and $\oint dz/z = 2\pi i$

Laurent series/isolated singularity

Estimating complex integral

Calculate the value of $\int_0^\infty \frac{\sqrt{x}\cos(\ln(x))}{x^2+1}\,dx$

How to calculate the arc part when using Residue theorem?

Integral of real part of $z$ around the unit circle

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