Question

Computing the principal value integral $\mathrm{p.v.}\int_0^\infty \frac{x}{(x^2 - 1)( e^{ax} - 1 )}\ dx$

score 111 · Answer 1 · 2026-03-25 12:07:04

111

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Computing the principal value integral $\mathrm{p.v.}\int_0^\infty \frac{x}{(x^2 - 1)( e^{ax} - 1 )}\ dx$

Published on 25 Mar 2026 - 12:07

score 287 · Answer 2 · 2026-02-23 16:59:17

287

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Contour integral $\int_{C_\varepsilon}\frac{e^{i\alpha\omega}}{\omega^2}\mathrm{d}\omega$

Published on 23 Feb 2026 - 16:59

score 390 · Answer 3 · 2026-03-24 19:55:35

390

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Sokhotski–Plemelj theorem for two-dimensional integrals

Published on 24 Mar 2026 - 19:55

score 175 · Answer 4 · 2026-03-24 22:58:21

175

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Definite integral with residues and a double pole

Published on 24 Mar 2026 - 22:58

score 576 · Answer 5 · 2026-03-25 01:39:08

576

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Residue theorem : Upper and Lower halfs

Published on 25 Mar 2026 - 1:39

score 98 · Answer 6 · 2026-03-25 03:37:00

98

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When can the Cauchy principal value be expressed as an improper integral?

Published on 25 Mar 2026 - 3:37

score 163 · Answer 7 · 2026-03-24 18:14:39

163

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Give a meaning to the integral $\int_{0}^{+\infty} \frac{\sec(x)}{1+x^2}\,dx$

Published on 24 Mar 2026 - 18:14

score 63 · Answer 8 · 2026-03-25 14:36:29

63

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Calculate the principal value $PV \int_{0}^{\pi} x^n \tan(x)\,dx, n=0,1,2,...$

Published on 25 Mar 2026 - 14:36

score 34 · Answer 9 · 2021-07-12 18:19:22

34

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Are there simple ways to "read off" the properties of a functions Hilbert transform

Published on 12 Jul 2021 - 18:19

score 126 · Answer 10 · 2021-07-13 23:35:56

126

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Differentiate under integral sign for Principal Value of $\int_{0}^{\infty}\frac{x^{a-1}}{1-x}dx$

Published on 13 Jul 2021 - 23:35

score 210 · Answer 11 · 2021-07-22 19:22:17

210

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Computing $\text{PV}\, \int_0^\infty (-1)^{\lfloor x\rfloor}\ln\left(\frac{\sqrt{x}\,e^x\,\Gamma(x)}{\sqrt{2\pi}\,x^x}\right)\,\mathrm{d}x$

Published on 22 Jul 2021 - 19:22

score 107 · Answer 12 · 2026-03-25 11:21:27

107

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Discrete random walk/risk process characterized by a step distribution with a heavy tail and a mean existing only as a Hadamard finite-part integral

Published on 25 Mar 2026 - 11:21

score 144 · Answer 13 · 2021-09-02 08:05:03

144

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Imaginary value of real principal value integral

Published on 02 Sep 2021 - 8:05

score 87 · Answer 14 · 2026-02-24 00:02:56

87

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Can we apply the Fundamental theorem of integration on $f(x)=\frac{1}{x}$

Published on 24 Feb 2026 - 0:02

score 43 · Answer 15 · 2021-10-10 15:11:58

43

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Primitive of Cauchy Principal Value?

Published on 10 Oct 2021 - 15:11

List Question

Computing the principal value integral $\mathrm{p.v.}\int_0^\infty \frac{x}{(x^2 - 1)( e^{ax} - 1 )}\ dx$

Contour integral $\int_{C_\varepsilon}\frac{e^{i\alpha\omega}}{\omega^2}\mathrm{d}\omega$

Sokhotski–Plemelj theorem for two-dimensional integrals

Definite integral with residues and a double pole

Residue theorem : Upper and Lower halfs

When can the Cauchy principal value be expressed as an improper integral?

Give a meaning to the integral $\int_{0}^{+\infty} \frac{\sec(x)}{1+x^2}\,dx$

Calculate the principal value $PV \int_{0}^{\pi} x^n \tan(x)\,dx, n=0,1,2,...$

Are there simple ways to "read off" the properties of a functions Hilbert transform

Differentiate under integral sign for Principal Value of $\int_{0}^{\infty}\frac{x^{a-1}}{1-x}dx$

Computing $\text{PV}\, \int_0^\infty (-1)^{\lfloor x\rfloor}\ln\left(\frac{\sqrt{x}\,e^x\,\Gamma(x)}{\sqrt{2\pi}\,x^x}\right)\,\mathrm{d}x$

Discrete random walk/risk process characterized by a step distribution with a heavy tail and a mean existing only as a Hadamard finite-part integral

Imaginary value of real principal value integral

Can we apply the Fundamental theorem of integration on $f(x)=\frac{1}{x}$

Primitive of Cauchy Principal Value?

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