Question

Evaluate : $\displaystyle\int\limits_{\gamma }\frac{\log (1+z)}{1+z}dz$

score 80 · Answer 1 · 2020-09-21 22:18:04

80

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Evaluate : $\displaystyle\int\limits_{\gamma }\frac{\log (1+z)}{1+z}dz$

Published on 21 Sep 2020 - 22:18

score 394 · Answer 2 · 2020-09-27 12:01:37

394

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Complex integration over a surface

Published on 27 Sep 2020 - 12:01

score 59 · Answer 3 · 2026-03-30 10:16:32

59

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How to show an integral of a complex function is analytic?

Published on 30 Mar 2026 - 10:16

score 68 · Answer 4 · 2026-02-23 08:56:35

68

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Asymptotic expansion for $\int e^{i\lambda x^2}e^{-x^2}x^j\text{d}x$

Published on 23 Feb 2026 - 8:56

score 59 · Answer 5 · 2020-09-29 01:53:23

59

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Complex integral $\int_C{e^{z^3}z^2}dz$ over a parameterized curve $z(t)=t+t^{10}i$

Published on 29 Sep 2020 - 1:53

score 124 · Answer 6 · 2020-09-29 19:04:11

124

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Magnitude of difference of two complex exponentials

Published on 29 Sep 2020 - 19:04

score 31 · Answer 7 · 2026-03-30 01:47:55

31

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Compute $\int_{x=-\infty} ^\infty \frac{\tanh (x)}{\prod_{k=1}^N (x-(x_k+i))}dx$

Published on 30 Mar 2026 - 1:47

score 112 · Answer 8 · 2020-10-03 08:10:24

112

Views

Integrating $\log(z − 1)/z^{n+1}$ anticlockwise around the unit circle.

Published on 03 Oct 2020 - 8:10

score 74 · Answer 9 · 2020-10-03 12:48:28

74

Views

How to integrate this function? $\int_{-1}^1 \frac{1}{\sqrt{1-x^2}(1+x^2)}\,dx$

Published on 03 Oct 2020 - 12:48

score 115 · Answer 10 · 2020-10-06 10:58:00

115

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Why I can change the order of summation and integral here?

Published on 06 Oct 2020 - 10:58

score 139 · Answer 11 · 2020-10-07 15:55:04

139

Views

When is a complex function orthogonal to its derivative

Published on 07 Oct 2020 - 15:55

score 141 · Answer 12 · 2020-10-10 20:46:18

141

Views

How can I calculate $\int_{-\infty}^{\infty}e^{-x^2}\cos(2bx)\,\mathrm{d}x$ using residue theorem?

Published on 10 Oct 2020 - 20:46

score 76 · Answer 13 · 2026-03-29 09:11:43

76

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Calculate $\oint_\gamma \frac{\ln(\overline{z} - b)}{z - a} dz$ using the Cauchy-Pompeiu formula

Published on 29 Mar 2026 - 9:11

score 481 · Answer 14 · 2026-03-29 11:02:11

481

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Computing $\int_{\alpha}\frac{1}{(z-a)^n(z-b)^m}dz$ using Cauchy integral formula

Published on 29 Mar 2026 - 11:02

score 224 · Answer 15 · 2026-03-25 15:22:45

224

Views

Establish an upper bound for $\zeta'(s)\over\zeta(s)$?

Published on 25 Mar 2026 - 15:22

List Question

Evaluate : $\displaystyle\int\limits_{\gamma }\frac{\log (1+z)}{1+z}dz$

Complex integration over a surface

How to show an integral of a complex function is analytic?

Asymptotic expansion for $\int e^{i\lambda x^2}e^{-x^2}x^j\text{d}x$

Complex integral $\int_C{e^{z^3}z^2}dz$ over a parameterized curve $z(t)=t+t^{10}i$

Magnitude of difference of two complex exponentials

Compute $\int_{x=-\infty} ^\infty \frac{\tanh (x)}{\prod_{k=1}^N (x-(x_k+i))}dx$

Integrating $\log(z − 1)/z^{n+1}$ anticlockwise around the unit circle.

How to integrate this function? $\int_{-1}^1 \frac{1}{\sqrt{1-x^2}(1+x^2)}\,dx$

Why I can change the order of summation and integral here?

When is a complex function orthogonal to its derivative

How can I calculate $\int_{-\infty}^{\infty}e^{-x^2}\cos(2bx)\,\mathrm{d}x$ using residue theorem?

Calculate $\oint_\gamma \frac{\ln(\overline{z} - b)}{z - a} dz$ using the Cauchy-Pompeiu formula

Computing $\int_{\alpha}\frac{1}{(z-a)^n(z-b)^m}dz$ using Cauchy integral formula

Establish an upper bound for $\zeta'(s)\over\zeta(s)$?

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