Question

If $r>0, c \in \mathbb{C}$, and $f$ analytic in an open neighborhood, then the integral of $\overline{f(z)}f’(z)$ is pure imaginary

score 22 · Answer 1 · 2023-10-14 19:03:29

22

Views

If $r>0, c \in \mathbb{C}$, and $f$ analytic in an open neighborhood, then the integral of $\overline{f(z)}f’(z)$ is pure imaginary

Published on 14 Oct 2023 - 19:03

score 65 · Answer 2 · 2023-10-15 00:29:19

If p is a non-constant polynomial and R>0 such that all roots of p lie inside $B_R(0)$, compute $\int_{B_R(0)} \frac{p’(z)}{p(z)}dz$

score 210 · Answer 3 · 2026-03-27 13:27:20

210

Views

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score 108 · Answer 4 · 2023-10-15 23:07:24

108

Views

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Published on 15 Oct 2023 - 23:07

score 76 · Answer 5 · 2023-10-16 19:24:50

76

Views

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score 31 · Answer 6 · 2023-10-19 08:27:19

31

Views

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score 32 · Answer 7 · 2023-10-21 22:18:06

32

Views

Let $\mu$ be the semicircle in the first two quadrants with radius $R$. Why is the length of $\mu\cap \{y > \sqrt{R} \}$ $\le 4\sqrt{\pi}$

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score 61 · Answer 8 · 2023-10-30 05:15:42

61

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score 317 · Answer 9 · 2023-11-03 21:57:37

317

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score 36 · Answer 10 · 2023-11-04 14:35:03

36

Views

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score 56 · Answer 11 · 2023-11-04 16:39:18

56

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score 78 · Answer 12 · 2023-11-05 19:30:32

78

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score 117 · Answer 13 · 2026-03-27 13:25:22

117

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score 72 · Answer 14 · 2023-11-07 16:54:50

72

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score 66 · Answer 15 · 2023-11-08 14:25:53

66

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List Question

If $r>0, c \in \mathbb{C}$, and $f$ analytic in an open neighborhood, then the integral of $\overline{f(z)}f’(z)$ is pure imaginary

If p is a non-constant polynomial and R>0 such that all roots of p lie inside $B_R(0)$, compute $\int_{B_R(0)} \frac{p’(z)}{p(z)}dz$

Can Cauchy's Theorem be used to solve a contour integral with singularities?

Can you show me how to evaluate this integral using residue theorem? I keep getting the wrong answer

Complex Analysis Integration involving log and branch cut

A question on something relating to analytic continuation of a $\Gamma()$-based function

Let $\mu$ be the semicircle in the first two quadrants with radius $R$. Why is the length of $\mu\cap \{y > \sqrt{R} \}$ $\le 4\sqrt{\pi}$

Contour integral principal branch

For holomorphic function $f: \Omega \to \mathbb{C}$ with $f^{(k)}(z_0) \in \mathbb{R}$ prove that $f(x) \in \mathbb{R}$ for every $(z_0 - r, z_0 +r)$

How to calculate the length of the image of the curve $\Gamma$?

Evaluating the integral $\int_C |\Bbb dz|/z$

Using Riemann's methods to derive the floor function of x from the zeta function

Understanding the role of domain in the question related to Cauchy theorem for complex integral

Evaluation of integral relating to the free scalar field theory

Integrating $z^n$ as a complex valued function

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