Question

Conjugate symmetry to prove inner product

score 2.8k · Answer 1 · 2016-01-27 18:45:53

2.8k

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Conjugate symmetry to prove inner product

Published on 27 Jan 2016 - 18:45

score 217 · Answer 2 · 2016-01-27 21:34:26

217

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Integration with Jordan's Lemma

Published on 27 Jan 2016 - 21:34

score 78 · Answer 3 · 2016-01-28 01:28:31

78

Views

Solutions of this integral $\int_{\gamma}\frac{e^{z^2}-1}{z\sin(z)}dz=0$

Published on 28 Jan 2016 - 1:28

score 165 · Answer 4 · 2016-02-03 07:53:57

165

Views

Compute the integrals using the residue theorem

Published on 03 Feb 2016 - 7:53

score 219 · Answer 5 · 2026-03-27 07:14:43

219

Views

A function that satisfies $|f(z)-\bar z|<0.9$ is not analytic in the unit circle.

Published on 27 Mar 2026 - 7:14

score 84 · Answer 6 · 2016-02-06 17:28:20

84

Views

Calculate $\int_{\left|z-1\right|=2}z^{n}\sin\left(z\right)dz$ for $n\in \mathbb{Z}$

Published on 06 Feb 2016 - 17:28

score 101 · Answer 7 · 2016-02-06 19:49:49

101

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Parametrize the given curve and compute the integral (complex numbers)

Published on 06 Feb 2016 - 19:49

score 6.6k · Answer 8 · 2016-02-06 21:09:45

6.6k

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Show that entire function $f$ is a polynomial of degree at most $n$

Published on 06 Feb 2016 - 21:09

score 644 · Answer 9 · 2016-02-06 22:02:37

644

Views

There is an entire function $g$ such that $f(z)=g\left(z^{n}\right)$.

Published on 06 Feb 2016 - 22:02

score 93 · Answer 10 · 2016-02-07 02:23:32

93

Views

Show that $g(z)=\frac{1}{n}\sum_{k=0}^{n-1} f \left(\xi^{k}\sqrt[n]{z}\right)$ is an entire function.

Published on 07 Feb 2016 - 2:23

score 94 · Answer 11 · 2016-02-07 09:51:12

Let $\gamma=\{z\in \Bbb C: \lvert z \rvert=2\}$ in anti-clockwise orientation. Then $I=\frac {1}{2\pi i} \int_{\gamma} z^7 \cos \frac 1{z^2} dz$=?

score 734 · Answer 12 · 2016-02-10 12:58:54

734

Views

Complex integration with infinitely many poles on imaginary axis

Published on 10 Feb 2016 - 12:58

score 42 · Answer 13 · 2016-02-10 17:39:19

42

Views

Writing a function $f : [-\pi,\pi) \to \mathbb{R}$ as $\sum c_k e^{ikx}$ where $c_k$ is to be found

Published on 10 Feb 2016 - 17:39

score 767 · Answer 14 · 2026-03-31 12:00:42

767

Views

Complex integration by substitution

Published on 31 Mar 2026 - 12:00

score 52 · Answer 15 · 2016-02-12 23:03:18

52

Views

If $f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^{n}$, then $c_{n}r^{n}=\frac{1}{2\pi}\int_{0}^{2\pi}f\left(z_{0}+re^{-2nt}\right)dt$

Published on 12 Feb 2016 - 23:03

List Question

Conjugate symmetry to prove inner product

Integration with Jordan's Lemma

Solutions of this integral $\int_{\gamma}\frac{e^{z^2}-1}{z\sin(z)}dz=0$

Compute the integrals using the residue theorem

A function that satisfies $|f(z)-\bar z|<0.9$ is not analytic in the unit circle.

Calculate $\int_{\left|z-1\right|=2}z^{n}\sin\left(z\right)dz$ for $n\in \mathbb{Z}$

Parametrize the given curve and compute the integral (complex numbers)

Show that entire function $f$ is a polynomial of degree at most $n$

There is an entire function $g$ such that $f(z)=g\left(z^{n}\right)$.

Show that $g(z)=\frac{1}{n}\sum_{k=0}^{n-1} f \left(\xi^{k}\sqrt[n]{z}\right)$ is an entire function.

Let $\gamma=\{z\in \Bbb C: \lvert z \rvert=2\}$ in anti-clockwise orientation. Then $I=\frac {1}{2\pi i} \int_{\gamma} z^7 \cos \frac 1{z^2} dz$=?

Complex integration with infinitely many poles on imaginary axis

Writing a function $f : [-\pi,\pi) \to \mathbb{R}$ as $\sum c_k e^{ikx}$ where $c_k$ is to be found

Complex integration by substitution

If $f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^{n}$, then $c_{n}r^{n}=\frac{1}{2\pi}\int_{0}^{2\pi}f\left(z_{0}+re^{-2nt}\right)dt$

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