Question

wrong answer in calculating the principal value of integral using complex analysis

score 47 · Answer 1 · 2026-03-22 12:34:28

47

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wrong answer in calculating the principal value of integral using complex analysis

Published on 22 Mar 2026 - 12:34

score 126 · Answer 2 · 2026-03-21 20:44:45

126

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Why does $PV\int_{0}^{\infty} dx \frac{e^{-x^2}}{(x-1)^2}$ have a finite answer?

Published on 21 Mar 2026 - 20:44

score 1.3k · Answer 3 · 2026-03-22 08:19:26

1.3k

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How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?

Published on 22 Mar 2026 - 8:19

score 188 · Answer 4 · 2026-03-22 09:18:41

188

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Troubles calculating $\mathrm{p.v.}\int_0^1\tan(\pi x)x\,dx$

Published on 22 Mar 2026 - 9:18

score 163 · Answer 5 · 2026-03-22 07:15:44

163

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Principal Value of a divergent integral over $\mathfrak{R}$

Published on 22 Mar 2026 - 7:15

score 121 · Answer 6 · 2026-03-22 01:52:35

121

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

Published on 22 Mar 2026 - 1:52

score 57 · Answer 7 · 2026-03-21 21:55:46

57

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Can we assign meaningful values to $\int_{-a}^bf(x)/x^n\,\mathrm dx$ for $n=2,3,\dots$

Published on 21 Mar 2026 - 21:55

score 112 · Answer 8 · 2026-03-25 15:17:53

112

Views

Did I find a generating function for assigning values to $\mathsf EX^{-n}$, $X\sim\mathcal N(\mu,\sigma^2)$, $n=1,2,\dots$?

Published on 25 Mar 2026 - 15:17

score 461 · Answer 9 · 2026-03-21 17:42:24

461

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Why do we care about Cauchy principal value?

Published on 21 Mar 2026 - 17:42

score 69 · Answer 10 · 2026-03-21 19:53:28

69

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Cauchy's Principal Value of $\int_{-\infty}^{\infty} \sin(x)/(a-x)dx$

Published on 21 Mar 2026 - 19:53

score 518 · Answer 11 · 2026-03-21 20:36:20

518

Views

Residue theorem: how to choose upper or lower half if only one pole exists

Published on 21 Mar 2026 - 20:36

score 1.1k · Answer 12 · 2026-03-22 01:17:49

1.1k

Views

How do we know that the Cauchy principal value gives the right answer in a calculation of $\int_{-\infty}^\infty\frac{\sin x}{x}dx$?

Published on 22 Mar 2026 - 1:17

score 117 · Answer 13 · 2026-03-21 21:03:27

117

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Evaluating Cauchy Principal value in Tricomi's formula

Published on 21 Mar 2026 - 21:03

score 60 · Answer 14 · 2026-03-22 01:18:51

60

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How to find $PV\left(\int _0^1\frac{\ln ^3\left(t\right)}{\left(1-t\right)\sqrt{2t-1}}\:dt\right)$

Published on 22 Mar 2026 - 1:18

score 381 · Answer 15 · 2026-03-22 13:33:15

381

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Calculate the principal value of $\int_{0}^\infty\frac{x^{(a-1)}}{1-x^b}dx$,where $0<a<b$

Published on 22 Mar 2026 - 13:33

List Question

wrong answer in calculating the principal value of integral using complex analysis

Why does $PV\int_{0}^{\infty} dx \frac{e^{-x^2}}{(x-1)^2}$ have a finite answer?

How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?

Troubles calculating $\mathrm{p.v.}\int_0^1\tan(\pi x)x\,dx$

Principal Value of a divergent integral over $\mathfrak{R}$

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

Can we assign meaningful values to $\int_{-a}^bf(x)/x^n\,\mathrm dx$ for $n=2,3,\dots$

Did I find a generating function for assigning values to $\mathsf EX^{-n}$, $X\sim\mathcal N(\mu,\sigma^2)$, $n=1,2,\dots$?

Why do we care about Cauchy principal value?

Cauchy's Principal Value of $\int_{-\infty}^{\infty} \sin(x)/(a-x)dx$

Residue theorem: how to choose upper or lower half if only one pole exists

How do we know that the Cauchy principal value gives the right answer in a calculation of $\int_{-\infty}^\infty\frac{\sin x}{x}dx$?

Evaluating Cauchy Principal value in Tricomi's formula

How to find $PV\left(\int _0^1\frac{\ln ^3\left(t\right)}{\left(1-t\right)\sqrt{2t-1}}\:dt\right)$

Calculate the principal value of $\int_{0}^\infty\frac{x^{(a-1)}}{1-x^b}dx$,where $0<a<b$

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