Question

Find $\int_{0}^{\infty} \frac{\sqrt{x}}{x^2+5x+6}$ using residues.

score 192 · Answer 1 · 2020-07-13 03:24:01

192

Views

Find $\int_{0}^{\infty} \frac{\sqrt{x}}{x^2+5x+6}$ using residues.

Published on 13 Jul 2020 - 3:24

score 188 · Answer 2 · 2020-07-15 12:13:14

188

Views

Find poles and residues of \begin{equation} f(z)=z^2/(\cosh z-1) \end{equation}

Published on 15 Jul 2020 - 12:13

score 60 · Answer 3 · 2020-07-15 18:20:57

60

Views

Integral of $u\,dx+v\,dy$ for a complex polynomial $f(z)=u+iv$

Published on 15 Jul 2020 - 18:20

score 94 · Answer 4 · 2026-03-27 12:56:06

94

Views

Primitives and the fundamental theorem of calculus for functions with poles

Published on 27 Mar 2026 - 12:56

score 81 · Answer 5 · 2026-03-27 04:35:14

81

Views

How to compute the residue of $\frac{1}{e^{\frac{1}{z}}-1}$ around $z=0$?

Published on 27 Mar 2026 - 4:35

score 199 · Answer 6 · 2020-07-21 15:40:43

199

Views

How does one show that the residue of the first derivative of a holomorphic function is zero in its singularity?

Published on 21 Jul 2020 - 15:40

score 33 · Answer 7 · 2020-07-22 15:52:49

33

Views

Proof of fourier transform expression

Published on 22 Jul 2020 - 15:52

score 235 · Answer 8 · 2020-07-23 01:59:28

235

Views

Residue Theorem Integral

Published on 23 Jul 2020 - 1:59

score 131 · Answer 9 · 2026-03-27 04:35:11

131

Views

Calculate residues at all isolated singularities of $f(z)=\frac{z^2+4}{(z+2)(z^2+1)^2}$.

Published on 27 Mar 2026 - 4:35

score 44 · Answer 10 · 2020-07-23 20:05:45

44

Views

Show that the residue is $c_{-1}=-\frac{q''(z_0)}{(q'(z_0))^3}$.

Published on 23 Jul 2020 - 20:05

score 72 · Answer 11 · 2020-07-27 18:44:56

72

Views

calculate $\int ^{\infty}_{0}\frac{x^a}{(x+b)^2}dx$ whereas $|a|<1,b>0$

Published on 27 Jul 2020 - 18:44

score 80 · Answer 12 · 2020-07-28 01:03:49

80

Views

Is $\oint_{\left | z \right |=2} \frac{e^{\frac{1}{z}}}{z(z^{2}+1))}dz$ equal to zero?

Published on 28 Jul 2020 - 1:03

score 263 · Answer 13 · 2020-07-28 01:57:46

263

Views

When does the small semicircular contribution in contour integrals (not) matter?

Published on 28 Jul 2020 - 1:57

score 122 · Answer 14 · 2026-03-26 14:34:54

122

Views

What is the correct choice of the contour in the case of undamped forced harmonic oscillator?

Published on 26 Mar 2026 - 14:34

score 196 · Answer 15 · 2020-07-29 14:47:02

196

Views

Complex analysis and Cauchy Residue theorem

Published on 29 Jul 2020 - 14:47

List Question

Find $\int_{0}^{\infty} \frac{\sqrt{x}}{x^2+5x+6}$ using residues.

Find poles and residues of \begin{equation} f(z)=z^2/(\cosh z-1) \end{equation}

Integral of $u\,dx+v\,dy$ for a complex polynomial $f(z)=u+iv$

Primitives and the fundamental theorem of calculus for functions with poles

How to compute the residue of $\frac{1}{e^{\frac{1}{z}}-1}$ around $z=0$?

How does one show that the residue of the first derivative of a holomorphic function is zero in its singularity?

Proof of fourier transform expression

Residue Theorem Integral

Calculate residues at all isolated singularities of $f(z)=\frac{z^2+4}{(z+2)(z^2+1)^2}$.

Show that the residue is $c_{-1}=-\frac{q''(z_0)}{(q'(z_0))^3}$.

calculate $\int ^{\infty}_{0}\frac{x^a}{(x+b)^2}dx$ whereas $|a|<1,b>0$

Is $\oint_{\left | z \right |=2} \frac{e^{\frac{1}{z}}}{z(z^{2}+1))}dz$ equal to zero?

When does the small semicircular contribution in contour integrals (not) matter?

What is the correct choice of the contour in the case of undamped forced harmonic oscillator?

Complex analysis and Cauchy Residue theorem

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