Question

Show that the derivatives of an analytic function cannot satisfy $|f^{(n)}(z)|>n!n^n$ for all $n$ for any $z$ where $f$ is analytic

score 658 · Answer 1 · 2026-03-28 00:49:12

658

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Show that the derivatives of an analytic function cannot satisfy $|f^{(n)}(z)|>n!n^n$ for all $n$ for any $z$ where $f$ is analytic

Published on 28 Mar 2026 - 0:49

score 44 · Answer 2 · 2016-02-28 09:36:59

44

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Showing a function is harmonic given some information

Published on 28 Feb 2016 - 9:36

score 102 · Answer 3 · 2016-02-28 21:11:26

102

Views

Prove that the following integral exists

Published on 28 Feb 2016 - 21:11

score 973 · Answer 4 · 2026-03-28 00:47:43

973

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How to evaluate the following complex integral

Published on 28 Mar 2026 - 0:47

score 229 · Answer 5 · 2016-02-29 03:59:19

229

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Evaluation of an improper integral with complex exponential

Published on 29 Feb 2016 - 3:59

score 837 · Answer 6 · 2016-03-01 21:37:31

837

Views

Proof using Cauchy Integral Theorem

Published on 01 Mar 2016 - 21:37

score 47 · Answer 7 · 2016-03-02 04:45:43

47

Views

Determining the integral of $f(z)\, dz$ and expressing the answer in terms of residue.

Published on 02 Mar 2016 - 4:45

score 2.2k · Answer 8 · 2016-03-02 11:52:51

2.2k

Views

Surface integral of complex function using residues

Published on 02 Mar 2016 - 11:52

score 62 · Answer 9 · 2016-03-02 16:13:47

62

Views

Show that $f'(a)=\frac{1}{2\pi}\int_0^{2\pi}\mathrm{e}^{-\mathrm{i}\theta}f(a+\mathrm{e}^{\mathrm{i}\theta})\mathrm{d}\theta$

Published on 02 Mar 2016 - 16:13

score 93 · Answer 10 · 2016-03-02 17:29:41

93

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Prove that the following function has a branch cut

Published on 02 Mar 2016 - 17:29

score 2.1k · Answer 11 · 2016-03-05 04:32:38

2.1k

Views

Variation of argument of a complex function

Published on 05 Mar 2016 - 4:32

score 214 · Answer 12 · 2016-03-06 09:36:23

214

Views

Integration of $\log z$ in complex analysis

Published on 06 Mar 2016 - 9:36

score 1k · Answer 13 · 2016-03-06 19:03:56

1k

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Determine the Integral $\int_{-\infty}^{\infty} e^{-x^2} \cos(2bx)dx$

Published on 06 Mar 2016 - 19:03

score 87 · Answer 14 · 2016-03-07 01:04:20

Proof integral:$\lim_{x \rightarrow +\infty} \int_0^{x} dx'e^{-i(k-k_0)x'} = \pi\delta(k-k_0) - P(\frac{i}{k-k_0})$,where $P$ stands for...

score 462 · Answer 15 · 2016-03-07 23:28:33

462

Views

Without Cauchy Integral Formula or Residues: $\int_{L}\frac{dz}{z^{2}+1}$

Published on 07 Mar 2016 - 23:28

List Question

Show that the derivatives of an analytic function cannot satisfy $|f^{(n)}(z)|>n!n^n$ for all $n$ for any $z$ where $f$ is analytic

Showing a function is harmonic given some information

Prove that the following integral exists

How to evaluate the following complex integral

Evaluation of an improper integral with complex exponential

Proof using Cauchy Integral Theorem

Determining the integral of $f(z)\, dz$ and expressing the answer in terms of residue.

Surface integral of complex function using residues

Show that $f'(a)=\frac{1}{2\pi}\int_0^{2\pi}\mathrm{e}^{-\mathrm{i}\theta}f(a+\mathrm{e}^{\mathrm{i}\theta})\mathrm{d}\theta$

Prove that the following function has a branch cut

Variation of argument of a complex function

Integration of $\log z$ in complex analysis

Determine the Integral $\int_{-\infty}^{\infty} e^{-x^2} \cos(2bx)dx$

Proof integral:$\lim_{x \rightarrow +\infty} \int_0^{x} dx'e^{-i(k-k_0)x'} = \pi\delta(k-k_0) - P(\frac{i}{k-k_0})$,where $P$ stands for...

Without Cauchy Integral Formula or Residues: $\int_{L}\frac{dz}{z^{2}+1}$

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