List questions from residue-calculus

Published on 27 Nov 2014 - 21:40

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Evaluating an Integral by Residue Theorem

Published on 01 Dec 2014 - 8:07

516

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Complex integral using cauchy residue formula

Published on 25 Mar 2026 - 9:33

564

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Finding $\sum_{n=1}^{\infty }\frac{243}{16(n\pi )^5}\sin(2n\pi /3)$

Published on 03 Dec 2014 - 19:53

84

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How can I calculate this complex integral?

Published on 28 Mar 2026 - 22:06

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Residue of $\frac{\cos(\frac{\pi}{z-1})}{z^2 \sin z}$ at $z=1$

Published on 05 Dec 2014 - 12:08

1.7k

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Find the contour integral around unit circle: $\int_{0}^{\pi}\frac{\cos2\phi}{1-2a \cos\phi + a^2} d\phi$ $where\;a\neq \pm1$

Published on 08 Dec 2014 - 6:08

1k

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How to solve $\int_0^{\infty}\frac{\cos{ax}}{x^3+1}dx$?

Published on 29 Mar 2026 - 2:54

777

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If $f(z)$ is a polynomial function of degree $n \ge 2$, prove that the sum of the residues of $\frac{1}{f(z)}$ is zero

Published on 09 Dec 2014 - 14:53

1.3k

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residue of this function at infinity

Published on 09 Dec 2014 - 15:27

100

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Poles of $\frac{1}{1+x^4}$

Published on 09 Dec 2014 - 22:35

300

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Evaluate $\int_{-\infty}^\infty \frac{1}{(x^2+1)^3} dx$

Published on 09 Dec 2014 - 22:44

331

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Evaluating $\int^{\infty }_{-\infty}\frac {z^3\sin az}{z^4+4}dz$

Published on 10 Dec 2014 - 1:53

199

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Countour integral using residue theorem: $ \int_{\gamma} \tanh(z) dz $ where $\gamma(t) = e^{it}$ and $0 \leq t \leq 2\pi$.

Published on 28 Mar 2026 - 2:24

976

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Generating function of the Laguerre Polynomials

Published on 10 Dec 2014 - 17:08

List Question

How to compute contour integral?

Evaluating an Integral by Residue Theorem

Complex integral using cauchy residue formula

Finding $\sum_{n=1}^{\infty }\frac{243}{16(n\pi )^5}\sin(2n\pi /3)$

How can I calculate this complex integral?

Residue of $\frac{\cos(\frac{\pi}{z-1})}{z^2 \sin z}$ at $z=1$

Find the contour integral around unit circle: $\int_{0}^{\pi}\frac{\cos2\phi}{1-2a \cos\phi + a^2} d\phi$ $where\;a\neq \pm1$

How to solve $\int_0^{\infty}\frac{\cos{ax}}{x^3+1}dx$?

If $f(z)$ is a polynomial function of degree $n \ge 2$, prove that the sum of the residues of $\frac{1}{f(z)}$ is zero

residue of this function at infinity

Poles of $\frac{1}{1+x^4}$

Evaluate $\int_{-\infty}^\infty \frac{1}{(x^2+1)^3} dx$

Evaluating $\int^{\infty }_{-\infty}\frac {z^3\sin az}{z^4+4}dz$

Countour integral using residue theorem: $ \int_{\gamma} \tanh(z) dz $ where $\gamma(t) = e^{it}$ and $0 \leq t \leq 2\pi$.

Generating function of the Laguerre Polynomials

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