Question

Residue at $\infty$ of $\frac{\sin(\pi z)}{z^2(z-1)}$ is $0$ but the residues of the only finite pole at $0$ is $-\pi$

score 114 · Answer 1 · 2026-04-09 16:59:06

114

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Residue at $\infty$ of $\frac{\sin(\pi z)}{z^2(z-1)}$ is $0$ but the residues of the only finite pole at $0$ is $-\pi$

Published on 09 Apr 2026 - 16:59

score 82 · Answer 2 · 2026-04-11 23:27:18

82

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Show the fourier transform of a function satisfies a differential equation

Published on 11 Apr 2026 - 23:27

score 239 · Answer 3 · 2022-07-24 22:47:27

239

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Proof Verification: $\int_{-1}^{1}\frac{\ln{(x+1)}}{x}dx = \frac{\pi^2}{4}$

Published on 24 Jul 2022 - 22:47

score 179 · Answer 4 · 2022-07-27 08:07:50

179

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Integrating $\int^{\infty}_0\frac{x^n}{e^x-1}\text{ d}x$ using contour integration only

Published on 27 Jul 2022 - 8:07

score 133 · Answer 5 · 2022-07-30 19:26:59

133

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Let $\gamma: [0,1] \to \{z \in \mathbb C: Im(z) \ge 0 \}$ be a closed and rectifiable path such that $\gamma(0) = 1, \gamma(1)=-1$ and ..

Published on 30 Jul 2022 - 19:26

score 112 · Answer 6 · 2022-07-31 09:39:04

112

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Contour Integral of $\frac{z^2+1}{z(z+2)}$

Published on 31 Jul 2022 - 9:39

score 209 · Answer 7 · 2026-03-27 22:31:13

209

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Find $f$ such that $f(f(x))=\log (x)$

Published on 27 Mar 2026 - 22:31

score 134 · Answer 8 · 2022-08-01 04:42:37

134

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If $f$ is an analytic function in $z=0$ and $g(z)=f(z^2)$, prove that $g^{(2n-1)}(0)=0$ for all $n\in\mathbb{Z}^+$.

Published on 01 Aug 2022 - 4:42

score 323 · Answer 9 · 2026-04-10 14:55:17

323

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How to use Mittag Leffler expansion (if possible) to solve the following integrals?

Published on 10 Apr 2026 - 14:55

score 103 · Answer 10 · 2022-08-06 15:48:56

103

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integral over ball in $\mathbb R^d$

Published on 06 Aug 2022 - 15:48

score 47 · Answer 11 · 2026-04-04 01:56:23

47

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Define the term $a_n$ in Laurent's series expansion $\sum_{n=-\infty}^{\infty} a_n(z-a)^n$ of $f$ centered on $z=a.$...

Published on 04 Apr 2026 - 1:56

score 82 · Answer 12 · 2022-08-09 23:54:42

82

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Why the antiderivative contains 2?

Published on 09 Aug 2022 - 23:54

score 283 · Answer 13 · 2026-04-09 04:58:41

283

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Understanding the use of Morera's Theorem

Published on 09 Apr 2026 - 4:58

score 175 · Answer 14 · 2022-08-14 02:49:39

175

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Showing that $\lim_{z\to0}z\,\frac{\cos(z/2)}{\sin(z/2)}=2$

Published on 14 Aug 2022 - 2:49

score 99 · Answer 15 · 2026-03-26 17:52:32

99

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Difficulty finding the principal value of $\int_{-\infty}^{\infty}\frac{\cos3x}{x-1}\,\mathrm{d}x$

Published on 26 Mar 2026 - 17:52

List Question

Residue at $\infty$ of $\frac{\sin(\pi z)}{z^2(z-1)}$ is $0$ but the residues of the only finite pole at $0$ is $-\pi$

Show the fourier transform of a function satisfies a differential equation

Proof Verification: $\int_{-1}^{1}\frac{\ln{(x+1)}}{x}dx = \frac{\pi^2}{4}$

Integrating $\int^{\infty}_0\frac{x^n}{e^x-1}\text{ d}x$ using contour integration only

Let $\gamma: [0,1] \to \{z \in \mathbb C: Im(z) \ge 0 \}$ be a closed and rectifiable path such that $\gamma(0) = 1, \gamma(1)=-1$ and ..

Contour Integral of $\frac{z^2+1}{z(z+2)}$

Find $f$ such that $f(f(x))=\log (x)$

If $f$ is an analytic function in $z=0$ and $g(z)=f(z^2)$, prove that $g^{(2n-1)}(0)=0$ for all $n\in\mathbb{Z}^+$.

How to use Mittag Leffler expansion (if possible) to solve the following integrals?

integral over ball in $\mathbb R^d$

Define the term $a_n$ in Laurent's series expansion $\sum_{n=-\infty}^{\infty} a_n(z-a)^n$ of $f$ centered on $z=a.$...

Why the antiderivative contains 2?

Understanding the use of Morera's Theorem

Showing that $\lim_{z\to0}z\,\frac{\cos(z/2)}{\sin(z/2)}=2$

Difficulty finding the principal value of $\int_{-\infty}^{\infty}\frac{\cos3x}{x-1}\,\mathrm{d}x$

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