Question

Prove that: $\frac{2\pi i}{(1 - e^{2i\pi/n})\prod_{k=0, k \neq 1}^{n-1} (e^{i\pi/n} - e^{i(2k-1)\pi/n})} = \frac{\pi/n}{\sin(\pi/n)}$

score 138 · Answer 1 · 2016-05-28 09:36:56

Prove that: $\frac{2\pi i}{(1 - e^{2i\pi/n})\prod_{k=0, k \neq 1}^{n-1} (e^{i\pi/n} - e^{i(2k-1)\pi/n})} = \frac{\pi/n}{\sin(\pi/n)}$

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score 366 · Answer 6 · 2016-06-04 11:24:26

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List Question

Prove that: $\frac{2\pi i}{(1 - e^{2i\pi/n})\prod_{k=0, k \neq 1}^{n-1} (e^{i\pi/n} - e^{i(2k-1)\pi/n})} = \frac{\pi/n}{\sin(\pi/n)}$

Evaluating the integral of $\frac{\cos(x) - e^{-x}}{x}$ using contour integration

Contour Integration along a line segment

Evaluating the real integral $\int_{0}^{2\pi}\frac{1}{2+\sin\theta}d\theta$ using complex analysis

How to find $L = \int_0^1 \frac{dx}{1+{x^8}}$

Evaluating $\int_{0}^\infty \frac{\log x \, dx}{\sqrt x(x^2+a^2)^2}$ using contour integration

Contour integral for finding $\int_0^\infty \frac{\ln x}{(x+a)^2+b^2} \, dx$

Complex analysis contour integration calculation!!

Contour Integral of $1/(zcos(z))$ around the circle $\lvert z \rvert = n\pi$

Contour Integral finding Poles

Prove that a square-integrable entire function is identically zero

Evaluating $\int_c\frac{1}{\sin\frac{1}{z}}\text{d}z$ over $C= \{z\big\vert|z|=\frac{1}{5}\}$

A variation of Ahmed's integral $\int_{0}^{1} \frac{(x^2+4)\sin^{-1}x}{x^4-12x^2+16} \, dx $

Maximum and minimum modulus principle

Contour integral independant of parametrisation

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