Question

Bounding complex contour integrals

score 113 · Answer 1 · 2026-04-29 23:46:44

Bounding complex contour integrals

Published on 29 Apr 2026 - 23:46

score 40 · Answer 2 · 2026-04-15 08:49:32

Let $\gamma,\sigma$ be differentiable closed curves. Prove that if $|\gamma(t)-\sigma(t)|<|\gamma(t)|$. Then $n(\gamma;0)=n(\sigma;0)$

score 72 · Answer 3 · 2026-04-30 02:06:09

72

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Question on Convergence of sequence

Published on 30 Apr 2026 - 2:06

score 185 · Answer 4 · 2026-04-13 17:19:19

185

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Integration of $\frac{1}{1+x^2+x^4+\cdots +x^{2m}}$

Published on 13 Apr 2026 - 17:19

score 67 · Answer 5 · 2026-04-16 16:01:30

67

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The order of zero at $ z=0$ of $ f(z) = \cos(z^3) - 1 $.

Published on 16 Apr 2026 - 16:01

score 194 · Answer 6 · 2026-03-25 07:42:13

194

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Contour integral on closed contour C that contains a singularity

Published on 25 Mar 2026 - 7:42

score 317 · Answer 7 · 2026-04-16 07:47:11

317

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Compute $\int_{|z|=1}\overline z^2$ $\sin z$ $\mathrm dz$

Published on 16 Apr 2026 - 7:47

score 262 · Answer 8 · 2026-03-25 07:41:12

262

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Closed contour integral that contains singularities

Published on 25 Mar 2026 - 7:41

score 150 · Answer 9 · 2026-04-14 13:24:02

150

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A nonconstant complex function satisfying $f(z+w)=f(z)f(w)$ and differentiable at the origin is entire

Published on 14 Apr 2026 - 13:24

score 140 · Answer 10 · 2026-04-12 05:26:02

140

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Integrating using residue theorem from minus infinity to infinity when there are zeroes on the real line

Published on 12 Apr 2026 - 5:26

score 537 · Answer 11 · 2026-04-16 13:39:29

537

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Show $f(z)=\int_{c} \frac{g(w)}{w-z}$ $dw$ is analytic on any domain $D$ not containing points of $C$

Published on 16 Apr 2026 - 13:39

score 152 · Answer 12 · 2026-04-17 03:17:47

152

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Fourier expansion of multiplicative analogue of Hecke operator

Published on 17 Apr 2026 - 3:17

score 45 · Answer 13 · 2026-04-12 07:10:42

45

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isolated singularity at 0, limit exists

Published on 12 Apr 2026 - 7:10

score 210 · Answer 14 · 2026-04-14 06:44:26

210

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Finding the remainder in Taylor series for complex functions

Published on 14 Apr 2026 - 6:44

score 71 · Answer 15 · 2026-04-13 20:54:36

71

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If $f(z) = u(z)+iv(z)$ is analytic, are both of $u(z)$ and $v(z)$ analytic?

Published on 13 Apr 2026 - 20:54

List Question

Bounding complex contour integrals

Let $\gamma,\sigma$ be differentiable closed curves. Prove that if $|\gamma(t)-\sigma(t)|<|\gamma(t)|$. Then $n(\gamma;0)=n(\sigma;0)$

Question on Convergence of sequence

Integration of $\frac{1}{1+x^2+x^4+\cdots +x^{2m}}$

The order of zero at $ z=0$ of $ f(z) = \cos(z^3) - 1 $.

Contour integral on closed contour C that contains a singularity

Compute $\int_{|z|=1}\overline z^2$ $\sin z$ $\mathrm dz$

Closed contour integral that contains singularities

A nonconstant complex function satisfying $f(z+w)=f(z)f(w)$ and differentiable at the origin is entire

Integrating using residue theorem from minus infinity to infinity when there are zeroes on the real line

Show $f(z)=\int_{c} \frac{g(w)}{w-z}$ $dw$ is analytic on any domain $D$ not containing points of $C$

Fourier expansion of multiplicative analogue of Hecke operator

isolated singularity at 0, limit exists

Finding the remainder in Taylor series for complex functions

If $f(z) = u(z)+iv(z)$ is analytic, are both of $u(z)$ and $v(z)$ analytic?

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