List questions from complex-integration

Published on 28 Mar 2026 - 2:48

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Prove that $\int_{0}^{\pi}e^{\cos(\theta)}\cos(\sin(\theta))\,d\theta = \pi$

Published on 21 Mar 2016 - 16:14

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Use Cauchy Inequalities to find an upper bound for $|f^4(i)|$ and $|f^4(0)|$

Published on 28 Mar 2026 - 2:44

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Evaluate using complex integration: $\int_{-\infty}^\infty \frac{dx}{(x^2+1)(x^2+9)}$

Published on 23 Mar 2016 - 0:05

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Complex analysis: Evaluate the integral

Published on 29 Mar 2026 - 3:18

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Let $f:U\rightarrow \mathbb{C}$ holomorphic no constant, then $\mbox{Re}f+\mbox{Im}f$ has no minimum in $U$.

Published on 23 Mar 2016 - 22:21

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Modulus of a Complex Logarithm

Published on 24 Mar 2016 - 1:52

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Question involving the Cauchy-Goursat Theorem

Published on 25 Mar 2016 - 20:23

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Confusion over complex integral along a path

Published on 28 Mar 2016 - 3:50

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Prove $\int_{-\infty}^{\infty} \frac{dx}{(1+x^2)^{n+1}} = \frac{(1)(3)(5)...(2n-1)}{(2)(4)(6)...(2n)} \pi \ \ \ \forall n \in \mathbb{N}$

Published on 28 Mar 2016 - 23:48

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Fourier transform of a Gaussian times a rational function

Published on 29 Mar 2016 - 9:18

262

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Fourier transform of Gaussian divided by a polynomial

Published on 29 Mar 2016 - 14:48

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Evaluating the integral $\int_{-\infty}^{\infty} \frac{(1-ix)^{n-s_1}}{(1+ix)^{n+s_2}} dx$.

Published on 29 Mar 2016 - 17:46

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Computing the residue of $\frac{\cot(\pi z)}{z^2}$ at pole $z=0$

Published on 30 Mar 2016 - 1:50

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Piecewise continuous contours with discontinuity only at end points

Published on 30 Mar 2016 - 2:32

List Question

For what simple piecewise smooth loops is this integral zero?

Prove that $\int_{0}^{\pi}e^{\cos(\theta)}\cos(\sin(\theta))\,d\theta = \pi$

Use Cauchy Inequalities to find an upper bound for $|f^4(i)|$ and $|f^4(0)|$

Evaluate using complex integration: $\int_{-\infty}^\infty \frac{dx}{(x^2+1)(x^2+9)}$

Complex analysis: Evaluate the integral

Let $f:U\rightarrow \mathbb{C}$ holomorphic no constant, then $\mbox{Re}f+\mbox{Im}f$ has no minimum in $U$.

Modulus of a Complex Logarithm

Question involving the Cauchy-Goursat Theorem

Confusion over complex integral along a path

Prove $\int_{-\infty}^{\infty} \frac{dx}{(1+x^2)^{n+1}} = \frac{(1)(3)(5)...(2n-1)}{(2)(4)(6)...(2n)} \pi \ \ \ \forall n \in \mathbb{N}$

Fourier transform of a Gaussian times a rational function

Fourier transform of Gaussian divided by a polynomial

Evaluating the integral $\int_{-\infty}^{\infty} \frac{(1-ix)^{n-s_1}}{(1+ix)^{n+s_2}} dx$.

Computing the residue of $\frac{\cot(\pi z)}{z^2}$ at pole $z=0$

Piecewise continuous contours with discontinuity only at end points

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