Question

Reducing this principal value integral to something I can evaluate numerically

score 101 · Answer 1 · 2026-04-23 15:18:03

101

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Reducing this principal value integral to something I can evaluate numerically

Published on 23 Apr 2026 - 15:18

score 490 · Answer 2 · 2026-05-10 09:22:26

490

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Bose-Einstein function as real part of polylogarithm: $\overline{G}_{s}(x)= \Re \mathrm{Li}_{s+1}(e^x)$

Published on 10 May 2026 - 9:22

score 1.1k · Answer 3 · 2026-05-07 08:11:01

1.1k

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Cauchy Principal Value and Divergent Integrals

Published on 07 May 2026 - 8:11

score 72 · Answer 4 · 2026-05-07 06:38:43

72

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What does the principal value $\mathscr{P}$ mean exactly in this integral?

Published on 07 May 2026 - 6:38

score 142 · Answer 5 · 2026-05-07 13:38:51

142

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Asymptotics of an integral $\mathscr{P} \int_{0}^{\infty} \frac{d\omega}{e^{\omega} - 1} \frac{\omega}{\omega^{2} - x^{2}}$ involving principal value

Published on 07 May 2026 - 13:38

score 323 · Answer 6 · 2026-05-02 20:25:17

323

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Help understanding the weak topology on the dual of the Schwartz space?

Published on 02 May 2026 - 20:25

score 190 · Answer 7 · 2026-05-07 04:46:41

190

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Evaluation of $\int_{-\infty}^{\infty} \frac{\sin(x)}{x^n} \,\mathrm{d}x $?

Published on 07 May 2026 - 4:46

score 410 · Answer 8 · 2026-05-07 09:42:00

410

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How to Calculate PV$\int_0^{\infty}\frac{\cos ax}{x^4-1}\:dx\: $for all a in R

Published on 07 May 2026 - 9:42

score 3k · Answer 9 · 2026-05-07 14:15:07

3k

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Principal value of 1/x

Published on 07 May 2026 - 14:15

score 141 · Answer 10 · 2026-04-23 09:11:32

141

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Principale value of complex integral

Published on 23 Apr 2026 - 9:11

score 155 · Answer 11 · 2026-04-25 08:28:05

155

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Existence of the Cauchy PV in the definition of logarithmic integral

Published on 25 Apr 2026 - 8:28

score 2.2k · Answer 12 · 2026-05-10 11:21:55

2.2k

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Find the principal value of $\big[\frac{e}{2}(-1-\sqrt3i)\big]^{3\pi i}$

Published on 10 May 2026 - 11:21

score 177 · Answer 13 · 2026-05-01 13:26:55

177

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Discontinuity across the cut of a function with a $\frac{1}{\sqrt{x^2-a}}$ factor

Published on 01 May 2026 - 13:26

score 173 · Answer 14 · 2026-05-10 11:20:59

173

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Approximating $I= \int\limits_0^1 \frac{1}{R^{2}-x^{2}} \exp (-\frac{a}{\sqrt{1-x^{2}}})\ dx$

Published on 10 May 2026 - 11:20

score 267 · Answer 15 · 2026-05-10 11:20:42

267

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An approach to evaluating a Cauchy principal value that yields unexpected extra imaginary term

Published on 10 May 2026 - 11:20

List Question

Reducing this principal value integral to something I can evaluate numerically

Bose-Einstein function as real part of polylogarithm: $\overline{G}_{s}(x)= \Re \mathrm{Li}_{s+1}(e^x)$

Cauchy Principal Value and Divergent Integrals

What does the principal value $\mathscr{P}$ mean exactly in this integral?

Asymptotics of an integral $\mathscr{P} \int_{0}^{\infty} \frac{d\omega}{e^{\omega} - 1} \frac{\omega}{\omega^{2} - x^{2}}$ involving principal value

Help understanding the weak topology on the dual of the Schwartz space?

Evaluation of $\int_{-\infty}^{\infty} \frac{\sin(x)}{x^n} \,\mathrm{d}x $?

How to Calculate PV$\int_0^{\infty}\frac{\cos ax}{x^4-1}\:dx\: $for all a in R

Principal value of 1/x

Principale value of complex integral

Existence of the Cauchy PV in the definition of logarithmic integral

Find the principal value of $\big[\frac{e}{2}(-1-\sqrt3i)\big]^{3\pi i}$

Discontinuity across the cut of a function with a $\frac{1}{\sqrt{x^2-a}}$ factor

Approximating $I= \int\limits_0^1 \frac{1}{R^{2}-x^{2}} \exp (-\frac{a}{\sqrt{1-x^{2}}})\ dx$

An approach to evaluating a Cauchy principal value that yields unexpected extra imaginary term

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