Question

Prove that $\int_{C_r} {f(z)}\,\mathrm dz→0$ if $r \rightarrow \infty$, where $C_r$ is the circle $|z-z_0|=r$

score 63 · Answer 1 · 2026-04-16 06:14:14

63

Views

Prove that $\int_{C_r} {f(z)}\,\mathrm dz→0$ if $r \rightarrow \infty$, where $C_r$ is the circle $|z-z_0|=r$

Published on 16 Apr 2026 - 6:14

score 208 · Answer 2 · 2026-04-29 12:06:04

208

Views

Winding number of a radius dependent function?

Published on 29 Apr 2026 - 12:06

score 187 · Answer 3 · 2026-05-11 07:15:21

187

Views

compute path integral using winding number

Published on 11 May 2026 - 7:15

score 101 · Answer 4 · 2026-04-16 09:37:04

101

Views

Name for integration technique of $\int_0^\infty \log^n(x)/R(x)\,dx$ via keyhole contour.

Published on 16 Apr 2026 - 9:37

score 173 · Answer 5 · 2026-05-13 19:42:26

173

Views

When/where to account for arguments/phases in branch cut problems?

Published on 13 May 2026 - 19:42

score 50 · Answer 6 · 2026-05-10 16:01:09

50

Views

Is this equality true? (cauchy integral + green's theorem)

Published on 10 May 2026 - 16:01

score 241 · Answer 7 · 2026-04-10 19:02:37

241

Views

When exactly is a path-Integral equal to 0 and when to apply Cauchy's Integral formula for derivatives

Published on 10 Apr 2026 - 19:02

score 142 · Answer 8 · 2026-04-12 20:51:46

142

Views

Terminology questions for the method of steepest descent

Published on 12 Apr 2026 - 20:51

score 873 · Answer 9 · 2026-05-10 18:59:20

873

Views

Proving upper bound $|\tan(z)| < 2$ on a contour

Published on 10 May 2026 - 18:59

score 300 · Answer 10 · 2026-04-10 08:59:49

300

Views

complex integration on a closed contour

Published on 10 Apr 2026 - 8:59

score 96 · Answer 11 · 2026-05-11 08:46:40

96

Views

Proving the growth theorem for functions of $S$

Published on 11 May 2026 - 8:46

score 185 · Answer 12 · 2026-04-15 07:31:46

Showing that $\frac{1}{2 \pi i} \oint_{\Psi_1} f(\zeta)\,d\zeta = \frac{1}{2 \pi i} \oint_{\Psi_2} f(\zeta)\,d\zeta$ via Cauchy-Goursat?

score 432 · Answer 13 · 2026-04-14 01:47:01

432

Views

Contour Integration of $\int_0^\infty \frac{\sin(ax)}{x}$

Published on 14 Apr 2026 - 1:47

score 220 · Answer 14 · 2026-05-14 07:46:02

220

Views

Evaluate $\int_{|z|=3}\frac{dz}{z^3(z^{10}-2)}$

Published on 14 May 2026 - 7:46

score 28 · Answer 15 · 2026-05-10 17:37:20

28

Views

Calculate contour integral of unknown functions

Published on 10 May 2026 - 17:37

List Question

Prove that $\int_{C_r} {f(z)}\,\mathrm dz→0$ if $r \rightarrow \infty$, where $C_r$ is the circle $|z-z_0|=r$

Winding number of a radius dependent function?

compute path integral using winding number

Name for integration technique of $\int_0^\infty \log^n(x)/R(x)\,dx$ via keyhole contour.

When/where to account for arguments/phases in branch cut problems?

Is this equality true? (cauchy integral + green's theorem)

When exactly is a path-Integral equal to 0 and when to apply Cauchy's Integral formula for derivatives

Terminology questions for the method of steepest descent

Proving upper bound $|\tan(z)| < 2$ on a contour

complex integration on a closed contour

Proving the growth theorem for functions of $S$

Showing that $\frac{1}{2 \pi i} \oint_{\Psi_1} f(\zeta)\,d\zeta = \frac{1}{2 \pi i} \oint_{\Psi_2} f(\zeta)\,d\zeta$ via Cauchy-Goursat?

Contour Integration of $\int_0^\infty \frac{\sin(ax)}{x}$

Evaluate $\int_{|z|=3}\frac{dz}{z^3(z^{10}-2)}$

Calculate contour integral of unknown functions

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