Question

Complex analysis, Jameson Exercise 2.1.1

score 66 · Answer 1 · 2026-03-27 11:45:32

66

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Complex analysis, Jameson Exercise 2.1.1

Published on 27 Mar 2026 - 11:45

score 65 · Answer 2 · 2023-06-28 22:15:47

65

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Application of generalized Cauchy integral theorem

Published on 28 Jun 2023 - 22:15

score 55 · Answer 3 · 2023-06-29 11:18:12

Show that $\lim\limits_{R\to 0}\int_{C_R}\frac{(z+1)dz}{(z^2+4)(z^2+9)}=0$, where $C_R$ is the semicircle $z=Re^{i\theta}, 0\leq\theta\leq\pi$.

score 51 · Answer 4 · 2026-04-02 12:25:31

51

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Closed form for $\int_0^{\infty} \frac{e^{-xt}\: t^{s-1}}{\sqrt{1-4at^2}}\: dt$.

Published on 02 Apr 2026 - 12:25

score 98 · Answer 5 · 2026-03-26 04:33:02

98

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Methods Of Counting Non-trivial Zeros Of Zeta Function

Published on 26 Mar 2026 - 4:33

score 51 · Answer 6 · 2023-07-09 15:42:19

51

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Using a different contour with $\int_{-\infty}^{\infty}{\frac{x^m}{1+x^n}\, dx}$

Published on 09 Jul 2023 - 15:42

score 91 · Answer 7 · 2026-04-03 11:06:41

91

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Estimating integral along arc in the contour integral $\int_{c}z^{a-1}e^{-c z}\,dz$

Published on 03 Apr 2026 - 11:06

score 115 · Answer 8 · 2023-07-11 01:50:34

115

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Complex Analysis: Does the closed curve of contour integral matter the result?

Published on 11 Jul 2023 - 1:50

score 41 · Answer 9 · 2026-03-29 20:17:35

41

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$f^{(n)}(z) \approx \frac{n!}{mr } \sum_{j=0}^{m-1} \frac{f( z+re^{i\frac{2\pi j}{m}} )}{e^{i\frac{2\pi j n }{m}} }$ did not work for $n\geq 2$

Published on 29 Mar 2026 - 20:17

score 135 · Answer 10 · 2023-07-13 22:21:18

135

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How to integrate $\int_{0}^{1}g'(x)f(g(x),x)dx$

Published on 13 Jul 2023 - 22:21

score 51 · Answer 11 · 2026-02-23 15:11:05

51

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let f be analytic in $Ball_2\left(0\right)$ and f is odd. let $U=\left\{z\in \mathbb{C}|1<\left|z\right|<2\right\}$, prove equality

Published on 23 Feb 2026 - 15:11

score 382 · Answer 12 · 2026-03-25 23:58:40

382

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Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

Published on 25 Mar 2026 - 23:58

score 56 · Answer 13 · 2026-03-28 10:33:04

56

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Contour integral over function $P(x)/Q(x)$: $P(x) = 1$ and $Q(x)$ can be broken into linear factors

Published on 28 Mar 2026 - 10:33

score 63 · Answer 14 · 2026-04-04 03:07:56

63

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Ci reflection formula

Published on 04 Apr 2026 - 3:07

score 122 · Answer 15 · 2026-03-26 11:01:24

122

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Series related to $\,_{2p+1}F_{2p}\left(\left\{\frac{a}{2}\right\}_{2p-1},a,\frac12;a+\frac{1}{2},\left\{1+\frac{a}{2}\right\}_{2p-1};1\right)$

Published on 26 Mar 2026 - 11:01

List Question

Complex analysis, Jameson Exercise 2.1.1

Application of generalized Cauchy integral theorem

Show that $\lim\limits_{R\to 0}\int_{C_R}\frac{(z+1)dz}{(z^2+4)(z^2+9)}=0$, where $C_R$ is the semicircle $z=Re^{i\theta}, 0\leq\theta\leq\pi$.

Closed form for $\int_0^{\infty} \frac{e^{-xt}\: t^{s-1}}{\sqrt{1-4at^2}}\: dt$.

Methods Of Counting Non-trivial Zeros Of Zeta Function

Using a different contour with $\int_{-\infty}^{\infty}{\frac{x^m}{1+x^n}\, dx}$

Estimating integral along arc in the contour integral $\int_{c}z^{a-1}e^{-c z}\,dz$

Complex Analysis: Does the closed curve of contour integral matter the result?

$f^{(n)}(z) \approx \frac{n!}{mr } \sum_{j=0}^{m-1} \frac{f( z+re^{i\frac{2\pi j}{m}} )}{e^{i\frac{2\pi j n }{m}} }$ did not work for $n\geq 2$

How to integrate $\int_{0}^{1}g'(x)f(g(x),x)dx$

let f be analytic in $Ball_2\left(0\right)$ and f is odd. let $U=\left\{z\in \mathbb{C}|1<\left|z\right|<2\right\}$, prove equality

Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

Contour integral over function $P(x)/Q(x)$: $P(x) = 1$ and $Q(x)$ can be broken into linear factors

Ci reflection formula

Series related to $\,_{2p+1}F_{2p}\left(\left\{\frac{a}{2}\right\}_{2p-1},a,\frac12;a+\frac{1}{2},\left\{1+\frac{a}{2}\right\}_{2p-1};1\right)$

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