Question

Fourier transform of Cauchy kernel

score 91 · Answer 1 · 2023-11-09 00:37:54

91

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Fourier transform of Cauchy kernel

Published on 09 Nov 2023 - 0:37

score 180 · Answer 2 · 2023-11-10 03:39:28

180

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If a holomorphic function $f$ from the open ball to the complex numbers have bounded derivative then $|\frac{f^{n}(0)}{n!}|\leq e$

Published on 10 Nov 2023 - 3:39

score 47 · Answer 3 · 2023-11-16 21:10:16

47

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Are the roots of the integrand inside the region for use in Residue Theorem?

Published on 16 Nov 2023 - 21:10

score 141 · Answer 4 · 2023-11-16 23:27:29

141

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Need help getting started on this Complex Integral.

Published on 16 Nov 2023 - 23:27

score 63 · Answer 5 · 2023-11-17 05:14:13

63

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Complex integral using residue theorem if there's no residue

Published on 17 Nov 2023 - 5:14

score 67 · Answer 6 · 2023-11-21 20:00:53

67

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Evaluating $\int_0^\infty x^{-s}\sin x\,\mathrm{d}x,\, 0 < \Re s < 2$

Published on 21 Nov 2023 - 20:00

score 226 · Answer 7 · 2023-11-22 21:54:10

226

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complex integral along rectangle

Published on 22 Nov 2023 - 21:54

score 159 · Answer 8 · 2023-11-26 04:13:21

159

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How to evaluate $ \displaystyle \int_0^\infty \frac {\sin x}{1+x^3}dx. $?

Published on 26 Nov 2023 - 4:13

score 69 · Answer 9 · 2023-12-02 21:41:33

69

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Is this the correct approach to finding this complex integral?

Published on 02 Dec 2023 - 21:41

score 86 · Answer 10 · 2023-12-04 15:38:49

86

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Complex derivative with respect to conjugate variable equal to the limit of a certain integral

Published on 04 Dec 2023 - 15:38

score 143 · Answer 11 · 2023-12-05 21:48:28

143

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Where did I go wrong with $\int{\frac{\ln{x}}{x + a}dx}$

Published on 05 Dec 2023 - 21:48

score 31 · Answer 12 · 2026-03-25 22:11:24

31

Views

Integrating along the closed contour crossing the branch cut

Published on 25 Mar 2026 - 22:11

score 78 · Answer 13 · 2023-12-08 20:55:57

78

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Prove that $\int_{0}^{\pi/2}\frac{d\theta}{a+\sin^2{\theta}}=\frac{\pi}{2\sqrt{a(a+1))}}$ , if a>0

Published on 08 Dec 2023 - 20:55

score 33 · Answer 14 · 2026-03-27 14:59:01

33

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Find the function rule of $g(z) = \int_{\alpha} \frac{w^3 + 2w}{(w-z)^3} dw$

Published on 27 Mar 2026 - 14:59

score 55 · Answer 15 · 2023-12-12 13:36:24

55

Views

Why if $\int_{\gamma} \frac{1}{z-a} dz=2k\pi i$ then $k$ is the number of windings?

Published on 12 Dec 2023 - 13:36

List Question

Fourier transform of Cauchy kernel

If a holomorphic function $f$ from the open ball to the complex numbers have bounded derivative then $|\frac{f^{n}(0)}{n!}|\leq e$

Are the roots of the integrand inside the region for use in Residue Theorem?

Need help getting started on this Complex Integral.

Complex integral using residue theorem if there's no residue

Evaluating $\int_0^\infty x^{-s}\sin x\,\mathrm{d}x,\, 0 < \Re s < 2$

complex integral along rectangle

How to evaluate $ \displaystyle \int_0^\infty \frac {\sin x}{1+x^3}dx. $?

Is this the correct approach to finding this complex integral?

Complex derivative with respect to conjugate variable equal to the limit of a certain integral

Where did I go wrong with $\int{\frac{\ln{x}}{x + a}dx}$

Integrating along the closed contour crossing the branch cut

Prove that $\int_{0}^{\pi/2}\frac{d\theta}{a+\sin^2{\theta}}=\frac{\pi}{2\sqrt{a(a+1))}}$ , if a>0

Find the function rule of $g(z) = \int_{\alpha} \frac{w^3 + 2w}{(w-z)^3} dw$

Why if $\int_{\gamma} \frac{1}{z-a} dz=2k\pi i$ then $k$ is the number of windings?

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