Question

Argument Principle-like complex integral involving logarithm

score 145 · Answer 1 · 2018-11-18 13:56:12

145

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Argument Principle-like complex integral involving logarithm

Published on 18 Nov 2018 - 13:56

score 56 · Answer 2 · 2026-03-24 23:51:34

56

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Prove simple closed curves $f$'s exist, so $\Gamma = C-\sum_{i=1}^{k}{f_i}$ satisfies $ \int_{\Gamma}{\frac{z^3e^{1/z}}{(z^2 + z + 1)(z^2 + 1)}dz}=0$

Published on 24 Mar 2026 - 23:51

score 58 · Answer 3 · 2018-11-19 00:27:45

58

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Complex integration lemma: shorter proof?

Published on 19 Nov 2018 - 0:27

score 12 · Answer 4 · 2026-02-27 21:52:49

12

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Is the role of the boxed condition $z'(t)\neq 0$ to avoid going back?

Published on 27 Feb 2026 - 21:52

score 40 · Answer 5 · 2018-11-19 17:21:46

40

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equality in integral inequality for compelx functions

Published on 19 Nov 2018 - 17:21

score 291 · Answer 6 · 2018-11-20 12:03:04

291

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Why is integral not equal to zero even though the path is closed?

Published on 20 Nov 2018 - 12:03

score 62 · Answer 7 · 2026-03-25 12:37:25

62

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Lineintegral $\int_{\gamma}|z|^2dz$ over ellipse

Published on 25 Mar 2026 - 12:37

score 482 · Answer 8 · 2018-11-21 04:27:18

482

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Contour integration - complex analysis: $\int_0^{\infty} \frac{\log^4(x)}{1+x^2} dx$

Published on 21 Nov 2018 - 4:27

score 372 · Answer 9 · 2018-11-22 14:58:32

372

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Does the specific contour matter when integrating over a closed loop

Published on 22 Nov 2018 - 14:58

score 502 · Answer 10 · 2018-11-22 15:17:35

502

Views

Evaluating the Integral of $\pi e^{\pi \overline z}$ with respect to $z$

Published on 22 Nov 2018 - 15:17

score 199 · Answer 11 · 2018-11-22 16:49:23

199

Views

Using the Cauchy Integral Theorem for Derivatives to evaluate an integral

Published on 22 Nov 2018 - 16:49

score 35 · Answer 12 · 2018-11-23 23:43:19

35

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Computation of complex valued integral

Published on 23 Nov 2018 - 23:43

score 1.1k · Answer 13 · 2026-03-25 11:06:23

1.1k

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Integration of $e^{ax}\cos^n bx$ and $e^{ax}\sin^n bx$

Published on 25 Mar 2026 - 11:06

score 3.1k · Answer 14 · 2018-11-26 11:19:37

3.1k

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What are we really doing when we integrate a complex exponential?

Published on 26 Nov 2018 - 11:19

score 854 · Answer 15 · 2018-11-27 10:48:22

854

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Calculate the integral of $\frac {\exp(z)}{\sin(z)}$ over $|z|=4$ using the residue theorem.

Published on 27 Nov 2018 - 10:48

List Question

Argument Principle-like complex integral involving logarithm

Prove simple closed curves $f$'s exist, so $\Gamma = C-\sum_{i=1}^{k}{f_i}$ satisfies $ \int_{\Gamma}{\frac{z^3e^{1/z}}{(z^2 + z + 1)(z^2 + 1)}dz}=0$

Complex integration lemma: shorter proof?

Is the role of the boxed condition $z'(t)\neq 0$ to avoid going back?

equality in integral inequality for compelx functions

Why is integral not equal to zero even though the path is closed?

Lineintegral $\int_{\gamma}|z|^2dz$ over ellipse

Contour integration - complex analysis: $\int_0^{\infty} \frac{\log^4(x)}{1+x^2} dx$

Does the specific contour matter when integrating over a closed loop

Evaluating the Integral of $\pi e^{\pi \overline z}$ with respect to $z$

Using the Cauchy Integral Theorem for Derivatives to evaluate an integral

Computation of complex valued integral

Integration of $e^{ax}\cos^n bx$ and $e^{ax}\sin^n bx$

What are we really doing when we integrate a complex exponential?

Calculate the integral of $\frac {\exp(z)}{\sin(z)}$ over $|z|=4$ using the residue theorem.

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