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 295 · Answer 1 · 2026-03-25 07:45:35

295

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 25 Mar 2026 - 7:45

score 494 · Answer 2 · 2026-03-25 06:12:08

494

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

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280

Views

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score 26 · Answer 4 · 2018-05-06 09:08:55

26

Views

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score 262 · Answer 5 · 2026-03-25 07:41:12

262

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1.2k

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score 85 · Answer 7 · 2018-05-09 01:15:56

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

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1.6k

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score 180 · Answer 9 · 2026-03-25 09:22:20

180

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78

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score 30 · Answer 11 · 2018-05-14 09:10:12

30

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score 37 · Answer 12 · 2018-05-14 16:52:44

37

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369

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905

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score 35 · Answer 15 · 2018-05-17 04:02:37

35

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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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