Question

Calculate $\int_0^{2\pi}{(\cos\theta+i\sin\theta\cos\phi)^l \cdot 2i\sin(m\phi)\,d\phi}$

score 54 · Answer 1 · 2023-03-10 16:01:17

54

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Calculate $\int_0^{2\pi}{(\cos\theta+i\sin\theta\cos\phi)^l \cdot 2i\sin(m\phi)\,d\phi}$

Published on 10 Mar 2023 - 16:01

score 95 · Answer 2 · 2026-02-23 06:21:57

95

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any suggestions for solving this integral involving a complex exponential of trigonometric functions?

Published on 23 Feb 2026 - 6:21

score 42 · Answer 3 · 2023-03-14 14:10:39

42

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How to find residue of the pole in this two variables complex function at y = 0?

Published on 14 Mar 2023 - 14:10

score 115 · Answer 4 · 2026-03-27 02:38:13

115

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Pole-skirting during contour integration when evaluating a Green's function

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score 141 · Answer 5 · 2023-03-16 22:56:14

141

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If $f$ is holomorphic on the closed unit disc, prove $\int_Cf(z)\log(z)dz=2\pi i\int_0^1f(x)dx$ where $C$ is the unit circle.

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score 303 · Answer 6 · 2023-03-19 13:00:56

303

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How to compute the area of the given region (NBHM $2022$)?

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score 46 · Answer 7 · 2026-03-25 15:38:55

46

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score 29 · Answer 8 · 2026-03-26 16:08:53

29

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score 60 · Answer 9 · 2026-03-27 10:16:41

60

Views

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Published on 27 Mar 2026 - 10:16

score 123 · Answer 10 · 2023-03-26 17:46:57

Is every simple closed contour in $\mathbb{C}$ the boundary of a compact set with the following property? (Two versions of Cauchy’s integral theorem)

score 32 · Answer 11 · 2023-03-27 06:42:34

32

Views

Elias Stein's complex analysis chapter 3 exercise 7

Published on 27 Mar 2023 - 6:42

score 273 · Answer 12 · 2026-03-27 18:27:36

273

Views

Prove that if $f$ has an isolated singularity at $z_0$ then the principal part of the Laurent series of $f$ at $z_0$ converges in $\mathbb C\ z_0$

Published on 27 Mar 2026 - 18:27

score 77 · Answer 13 · 2023-03-30 10:58:24

77

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How to write functions in terms of the Fox H-function?

Published on 30 Mar 2023 - 10:58

score 141 · Answer 14 · 2023-03-31 05:18:02

141

Views

Find $\lim_{z\to 1+i}\left(\frac{z+2-i}{3}\right)^\frac{z-i}{z-1-i}$

Published on 31 Mar 2023 - 5:18

score 65 · Answer 15 · 2023-04-02 09:41:34

65

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Solving $2$ dimensional inverse Fourier transform

Published on 02 Apr 2023 - 9:41

List Question

Calculate $\int_0^{2\pi}{(\cos\theta+i\sin\theta\cos\phi)^l \cdot 2i\sin(m\phi)\,d\phi}$

any suggestions for solving this integral involving a complex exponential of trigonometric functions?

How to find residue of the pole in this two variables complex function at y = 0?

Pole-skirting during contour integration when evaluating a Green's function

If $f$ is holomorphic on the closed unit disc, prove $\int_Cf(z)\log(z)dz=2\pi i\int_0^1f(x)dx$ where $C$ is the unit circle.

How to compute the area of the given region (NBHM $2022$)?

Preforming an explicit inverse Mellin transform

Evaluating tricky definite complex integral and getting numerical result as a single complex number

Example for complex integral

Is every simple closed contour in $\mathbb{C}$ the boundary of a compact set with the following property? (Two versions of Cauchy’s integral theorem)

Elias Stein's complex analysis chapter 3 exercise 7

Prove that if $f$ has an isolated singularity at $z_0$ then the principal part of the Laurent series of $f$ at $z_0$ converges in $\mathbb C\ z_0$

How to write functions in terms of the Fox H-function?

Find $\lim_{z\to 1+i}\left(\frac{z+2-i}{3}\right)^\frac{z-i}{z-1-i}$

Solving $2$ dimensional inverse Fourier transform

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