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Complex entire functions without taking values on a segment are constant!

score 1k · Answer 1 · 2026-03-26 17:29:20

1k

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Complex entire functions without taking values on a segment are constant!

Published on 26 Mar 2026 - 17:29

score 4.1k · Answer 2 · 2015-04-06 02:38:51

4.1k

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Contour Integral of $\log(z)/(1+z^a)$ where $a\gt1$

Published on 06 Apr 2015 - 2:38

score 56 · Answer 3 · 2015-04-06 13:18:10

56

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Equality concerning a certain complex integration

Published on 06 Apr 2015 - 13:18

score 71 · Answer 4 · 2015-04-07 15:49:49

71

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Any idea how to evaluate this equation?

Published on 07 Apr 2015 - 15:49

score 615 · Answer 5 · 2015-04-09 04:33:19

615

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How do I use residue theorem to evaluate this improper integral to get a good looking solution?

Published on 09 Apr 2015 - 4:33

score 70 · Answer 6 · 2015-04-11 19:49:05

70

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Evaluate the integral $\int_0^\infty\frac{x^a\ln{x}}{x+b} \, dx$

Published on 11 Apr 2015 - 19:49

score 231 · Answer 7 · 2015-04-12 23:08:39

231

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How to compute the following real integrals using the residue theorem?

Published on 12 Apr 2015 - 23:08

score 214 · Answer 8 · 2015-04-13 15:46:25

214

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Trying to understand a proof in Rudin concerning winding number

Published on 13 Apr 2015 - 15:46

score 1.3k · Answer 9 · 2026-03-26 16:06:26

1.3k

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Are the integrals of the following function path independent in the following domain?

Published on 26 Mar 2026 - 16:06

score 88 · Answer 10 · 2015-04-14 15:22:29

88

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show that $\int_0^{\infty}\ln(2x)\frac{ax-u(1-e^{-2ax})}{\sinh^2(ax)}x^{2u-1}dx=\frac{1}{2u}(\frac{\pi}{a})^{2u}|B_{2u}|:u \in N$

Published on 14 Apr 2015 - 15:22

score 437 · Answer 11 · 2026-03-25 09:48:58

437

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Contour integration with a branch cut. Parameterizing f(z) properly

Published on 25 Mar 2026 - 9:48

score 402 · Answer 12 · 2015-04-17 12:35:56

402

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How to use Cauchy's integral formula with more than one pole?

Published on 17 Apr 2015 - 12:35

score 946 · Answer 13 · 2015-04-18 01:14:25

946

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Characteristic Function and Density Function

Published on 18 Apr 2015 - 1:14

score 64 · Answer 14 · 2015-04-20 12:00:44

64

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Calculate complex integral $\int_\Gamma\frac{\ln(z+5)}{z^3+iz^2+6z}$

Published on 20 Apr 2015 - 12:00

score 1.6k · Answer 15 · 2015-04-20 18:47:07

1.6k

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Use Cauchy's Integral Formula to evaluate the following integrals.

Published on 20 Apr 2015 - 18:47

List Question

Complex entire functions without taking values on a segment are constant!

Contour Integral of $\log(z)/(1+z^a)$ where $a\gt1$

Equality concerning a certain complex integration

Any idea how to evaluate this equation?

How do I use residue theorem to evaluate this improper integral to get a good looking solution?

Evaluate the integral $\int_0^\infty\frac{x^a\ln{x}}{x+b} \, dx$

How to compute the following real integrals using the residue theorem?

Trying to understand a proof in Rudin concerning winding number

Are the integrals of the following function path independent in the following domain?

show that $\int_0^{\infty}\ln(2x)\frac{ax-u(1-e^{-2ax})}{\sinh^2(ax)}x^{2u-1}dx=\frac{1}{2u}(\frac{\pi}{a})^{2u}|B_{2u}|:u \in N$

Contour integration with a branch cut. Parameterizing f(z) properly

How to use Cauchy's integral formula with more than one pole?

Characteristic Function and Density Function

Calculate complex integral $\int_\Gamma\frac{\ln(z+5)}{z^3+iz^2+6z}$

Use Cauchy's Integral Formula to evaluate the following integrals.

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