Question

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

score 296 · Answer 1 · 2026-05-10 15:30:28

296

Views

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Published on 10 May 2026 - 15:30

score 495 · Answer 2 · 2026-05-10 12:35:02

495

Views

Using Contour Integration to Prove $\lim_{\epsilon\to 0^{+}}\int_{-1}^{1}x^{\epsilon-1}\,\mathrm{d}x=-\pi\mathrm{i}$

Published on 10 May 2026 - 12:35

score 282 · Answer 3 · 2026-05-10 15:28:48

282

Views

Gaussian integral over a wedge of the complex plane

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score 29 · Answer 4 · 2026-04-16 11:46:04

29

Views

Primitive of $ z \longmapsto (z-z_0)^k $ in $ \mathbb{C} \backslash \{z_0 \}.$

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score 263 · Answer 5 · 2026-05-10 15:27:48

263

Views

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score 1.2k · Answer 6 · 2026-04-16 12:52:58

1.2k

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score 88 · Answer 7 · 2026-04-16 05:55:31

Let $\gamma_r(t) = 1+re^{it}$ for $0\leq t \leq \pi/4$. Calculate $\lim\limits_{r\rightarrow 0+} \int_{\gamma_r} \frac{\cos (\pi z)}{\log z}$

score 1.6k · Answer 8 · 2026-04-12 13:17:13

1.6k

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score 182 · Answer 9 · 2026-05-10 15:26:45

182

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score 81 · Answer 10 · 2026-04-09 12:25:42

81

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score 33 · Answer 11 · 2026-04-16 23:36:06

33

Views

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score 40 · Answer 12 · 2026-04-11 02:45:55

40

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371

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score 910 · Answer 14 · 2026-05-10 12:53:34

910

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score 38 · Answer 15 · 2026-04-09 08:06:22

38

Views

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Published on 09 Apr 2026 - 8:06

List Question

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Using Contour Integration to Prove $\lim_{\epsilon\to 0^{+}}\int_{-1}^{1}x^{\epsilon-1}\,\mathrm{d}x=-\pi\mathrm{i}$

Gaussian integral over a wedge of the complex plane

Primitive of $ z \longmapsto (z-z_0)^k $ in $ \mathbb{C} \backslash \{z_0 \}.$

Closed contour integral that contains singularities

Evaluating $ \int_0^\pi \frac{\cos{n\theta}}{1 -2r\cos{\theta}+r^2} d\theta $

Let $\gamma_r(t) = 1+re^{it}$ for $0\leq t \leq \pi/4$. Calculate $\lim\limits_{r\rightarrow 0+} \int_{\gamma_r} \frac{\cos (\pi z)}{\log z}$

$\int_{0}^{2\pi} \frac{1}{5-3sin(\theta)} d\theta$ - Need Help Finding Mistake

complex integral over a closed path.

Residue integral over an arc

Solve $\int_L \frac{1}{z} dz$ with L going from $1 \rightarrow1+i \rightarrow-1+i\rightarrow-1-i\rightarrow2-i\rightarrow2$

Residue of a point defined by a function

Contour deformation in several variables

Peskin & Schroeder equation 2.54 clarification

Fourier serier with complex integral

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