Question

$ind_{\Gamma}(0)f(z)=\frac{1}{2\pi i}\int_{\Gamma}\frac{zf(w)}{w(z-w)}dw$

score 158 · Answer 1 · 2022-05-31 14:10:58

158

Views

$ind_{\Gamma}(0)f(z)=\frac{1}{2\pi i}\int_{\Gamma}\frac{zf(w)}{w(z-w)}dw$

Published on 31 May 2022 - 14:10

score 63 · Answer 2 · 2022-06-05 13:24:40

63

Views

Contour integration in complex analysis

Published on 05 Jun 2022 - 13:24

score 55 · Answer 3 · 2022-06-14 14:52:44

55

Views

Estimation of $\lvert f' \rvert$ via Cauchy-integral formula

Published on 14 Jun 2022 - 14:52

score 70 · Answer 4 · 2026-03-25 16:44:21

70

Views

Evaluate $\int_{0}^{\infty}\cos(t^{2})dt$ and $\int_{0}^{\infty}\sin(t^{2})dt$ using Cauchy‘s theorem

Published on 25 Mar 2026 - 16:44

score 122 · Answer 5 · 2022-06-16 08:20:39

122

Views

Evaluating $\int_{-\infty}^{\infty} e^{i \lambda x} \frac{\sinh ax}{\sinh \pi x} dx $ using complex analysis

Published on 16 Jun 2022 - 8:20

score 42 · Answer 6 · 2022-06-22 06:19:50

42

Views

Some relations that an analytic/ entire function will satisfy

Published on 22 Jun 2022 - 6:19

score 443 · Answer 7 · 2022-06-24 06:46:05

443

Views

Complex Analysis to solve this integral? $\int_0^{\pi/2} \frac{\ln(\sin(x))}{\sqrt{1 + \cos^2(x)}}\text{d}x$

Published on 24 Jun 2022 - 6:46

score 100 · Answer 8 · 2022-06-29 15:28:09

100

Views

Need help on solving the limit of a contour integral of a semicircle around $z = 0$ as the radius $\to \infty$

Published on 29 Jun 2022 - 15:28

score 82 · Answer 9 · 2022-06-29 20:06:36

82

Views

Confused about Cauchy Integral Theorem

Published on 29 Jun 2022 - 20:06

score 97 · Answer 10 · 2022-07-15 12:36:20

97

Views

If $f$ is entire and $\lim_\limits{z\to\infty} e^{f(z)} = 4$, show that $f$ is constant

Published on 15 Jul 2022 - 12:36

score 56 · Answer 11 · 2022-07-15 13:36:40

56

Views

Problem understanding the Cauchy's integral theorem

Published on 15 Jul 2022 - 13:36

score 213 · Answer 12 · 2022-08-10 20:14:28

213

Views

Given a laurent series, how do we show it doesnt have a pole?

Published on 10 Aug 2022 - 20:14

score 45 · Answer 13 · 2022-08-11 15:38:39

45

Views

Show that a domain is convex or that a path is homologous to zero

Published on 11 Aug 2022 - 15:38

score 137 · Answer 14 · 2022-08-28 21:19:13

137

Views

Understanding the proof of Cauchy's Estimate.

Published on 28 Aug 2022 - 21:19

score 30 · Answer 15 · 2022-09-06 16:08:32

30

Views

Evaluate $\int\frac{\sin z}{z^2(z^2+4)} dz$ in the region $|z - i| = 2$ using Cauchy Integral Formula.

Published on 06 Sep 2022 - 16:08

List Question

$ind_{\Gamma}(0)f(z)=\frac{1}{2\pi i}\int_{\Gamma}\frac{zf(w)}{w(z-w)}dw$

Contour integration in complex analysis

Estimation of $\lvert f' \rvert$ via Cauchy-integral formula

Evaluate $\int_{0}^{\infty}\cos(t^{2})dt$ and $\int_{0}^{\infty}\sin(t^{2})dt$ using Cauchy‘s theorem

Evaluating $\int_{-\infty}^{\infty} e^{i \lambda x} \frac{\sinh ax}{\sinh \pi x} dx $ using complex analysis

Some relations that an analytic/ entire function will satisfy

Complex Analysis to solve this integral? $\int_0^{\pi/2} \frac{\ln(\sin(x))}{\sqrt{1 + \cos^2(x)}}\text{d}x$

Need help on solving the limit of a contour integral of a semicircle around $z = 0$ as the radius $\to \infty$

Confused about Cauchy Integral Theorem

If $f$ is entire and $\lim_\limits{z\to\infty} e^{f(z)} = 4$, show that $f$ is constant

Problem understanding the Cauchy's integral theorem

Given a laurent series, how do we show it doesnt have a pole?

Show that a domain is convex or that a path is homologous to zero

Understanding the proof of Cauchy's Estimate.

Evaluate $\int\frac{\sin z}{z^2(z^2+4)} dz$ in the region $|z - i| = 2$ using Cauchy Integral Formula.

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