Question

Computing $\int_0^\infty \exp\left( -\frac{x^2}{A} -\frac{B}{x} -Cx \right){\rm d}x$

score 175 · Answer 1 · 2021-03-08 12:22:36

175

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Computing $\int_0^\infty \exp\left( -\frac{x^2}{A} -\frac{B}{x} -Cx \right){\rm d}x$

Published on 08 Mar 2021 - 12:22

score 475 · Answer 2 · 2026-04-03 19:36:53

475

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Integration by parts on the Riemann sphere

Published on 03 Apr 2026 - 19:36

score 270 · Answer 3 · 2021-03-10 16:26:07

270

Views

Prove that $\lim_{r \to 0} \frac{1}{r^2} \int_{|z| =r} f(z)dz = 2\pi i\frac{\partial f}{\partial \overline z}(0) $.

Published on 10 Mar 2021 - 16:26

score 57 · Answer 4 · 2021-03-13 08:56:19

57

Views

The antiderivative of $\frac{1}{x-ib}$

Published on 13 Mar 2021 - 8:56

score 40 · Answer 5 · 2021-03-13 15:58:30

40

Views

Double complex integral with a multivariable pole

Published on 13 Mar 2021 - 15:58

score 30 · Answer 6 · 2021-03-14 11:01:43

30

Views

Range of convergence for a Gaussian in the complex plane

Published on 14 Mar 2021 - 11:01

score 122 · Answer 7 · 2026-03-26 21:25:59

122

Views

Cauchy principal value for an integral with poles on path of integration

Published on 26 Mar 2026 - 21:25

score 595 · Answer 8 · 2021-03-15 08:39:42

595

Views

Integrate $f(z)=\frac{\pi\cot\pi z}{(u+z)^2}$

Published on 15 Mar 2021 - 8:39

score 199 · Answer 9 · 2021-03-18 18:01:44

199

Views

What is the maximum possible number of solutions of the equation $ f (z) = az + b$, as $a $ and $b$ vary over complex numbers?

Published on 18 Mar 2021 - 18:01

score 99 · Answer 10 · 2021-03-22 00:44:46

99

Views

How to you evaluate ${\int \frac{1}{z\left(z-1\right)\left(z-3\right)}dz}$ using the Residue Theorem

Published on 22 Mar 2021 - 0:44

score 229 · Answer 11 · 2021-03-22 23:39:02

229

Views

Prove this Cauchy integral $\oint_C \frac{f'(z)}{z-z_0}dz = \oint_C \frac{f(z)}{(z-z_0)^2}dz$

Published on 22 Mar 2021 - 23:39

score 77 · Answer 12 · 2026-04-03 00:31:39

77

Views

Solve with Cauchy Integral theorem: $\oint_C \frac{1}{z(2z+1)^2} \, \text{d}z$ but solve with partial fractions

Published on 03 Apr 2026 - 0:31

score 59 · Answer 13 · 2021-03-23 18:59:42

59

Views

Using Cauchy Integral, solve: $\oint_C \frac{1}{(2z+1)^2}dz$ without use residue theorem

Published on 23 Mar 2021 - 18:59

score 175 · Answer 14 · 2021-03-24 07:29:27

175

Views

Contour integral of $\displaystyle\oint_{c} \frac{e^{ix}}{1+z^{2}} dz$

Published on 24 Mar 2021 - 7:29

score 75 · Answer 15 · 2021-03-25 06:29:51

75

Views

What's wrong with my solution for this complex integral?

Published on 25 Mar 2021 - 6:29

List Question

Computing $\int_0^\infty \exp\left( -\frac{x^2}{A} -\frac{B}{x} -Cx \right){\rm d}x$

Integration by parts on the Riemann sphere

Prove that $\lim_{r \to 0} \frac{1}{r^2} \int_{|z| =r} f(z)dz = 2\pi i\frac{\partial f}{\partial \overline z}(0) $.

The antiderivative of $\frac{1}{x-ib}$

Double complex integral with a multivariable pole

Range of convergence for a Gaussian in the complex plane

Cauchy principal value for an integral with poles on path of integration

Integrate $f(z)=\frac{\pi\cot\pi z}{(u+z)^2}$

What is the maximum possible number of solutions of the equation $ f (z) = az + b$, as $a $ and $b$ vary over complex numbers?

How to you evaluate ${\int \frac{1}{z\left(z-1\right)\left(z-3\right)}dz}$ using the Residue Theorem

Prove this Cauchy integral $\oint_C \frac{f'(z)}{z-z_0}dz = \oint_C \frac{f(z)}{(z-z_0)^2}dz$

Solve with Cauchy Integral theorem: $\oint_C \frac{1}{z(2z+1)^2} \, \text{d}z$ but solve with partial fractions

Using Cauchy Integral, solve: $\oint_C \frac{1}{(2z+1)^2}dz$ without use residue theorem

Contour integral of $\displaystyle\oint_{c} \frac{e^{ix}}{1+z^{2}} dz$

What's wrong with my solution for this complex integral?

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