List questions from cauchy-principal-value

Published on 22 Mar 2026 - 21:51

194

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Integral Along Positive Real Axis in the Presence of a Branch Cut: $\int_0^\infty dt \frac{\exp(-t/\alpha)}{(p - bt)^q}$

Published on 25 Mar 2026 - 11:21

3.4k

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Cauchy integral indented contour question: $\int_{-\infty}^\infty \frac{(x+1)^2}{x(x^2+4)^2}dx$

Published on 23 Mar 2026 - 11:13

1.9k

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Can you explain us a simple example, for a mathematical function, of Kramers–Kronig relations?

Published on 23 Mar 2026 - 9:37

392

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Principal value of complete elliptic integral of third kind

Published on 23 Mar 2026 - 0:18

61

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limits equality

Published on 23 Mar 2026 - 3:01

217

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Principal value of Carlson elliptic integral $R_C$

Published on 23 Mar 2026 - 6:36

214

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Definite integral involving trigonometric functions and algebraic function

Published on 23 Mar 2026 - 4:15

498

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Is there a reason to prefer the improper integral for some cases over the Cauchy principal value?

Published on 23 Mar 2026 - 4:42

141

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Cauchy principal value

Published on 23 Mar 2026 - 9:38

58

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doubt in calculation of limits

Published on 23 Mar 2026 - 14:35

110

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Problem computing a Cauchy principle value

Published on 22 Mar 2026 - 16:33

79

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complex integral and singularity

Published on 23 Mar 2026 - 12:06

107

Views

Should $p.v.\int_0^1 x\cot(\pi x)dx$ converge?

Published on 22 Mar 2026 - 18:21

104

Views

An explanation or hints to evaluate $\text{PV}\int_0^\infty \frac{e^{-x}(x+\log (x))}{1-e^{-x}}dx$

Published on 23 Mar 2026 - 6:04

List Question

Integration of an improper integral and the Cauchy principal value

Integral Along Positive Real Axis in the Presence of a Branch Cut: $\int_0^\infty dt \frac{\exp(-t/\alpha)}{(p - bt)^q}$

Cauchy integral indented contour question: $\int_{-\infty}^\infty \frac{(x+1)^2}{x(x^2+4)^2}dx$

Can you explain us a simple example, for a mathematical function, of Kramers–Kronig relations?

Principal value of complete elliptic integral of third kind

limits equality

Principal value of Carlson elliptic integral $R_C$

Definite integral involving trigonometric functions and algebraic function

Is there a reason to prefer the improper integral for some cases over the Cauchy principal value?

Cauchy principal value

doubt in calculation of limits

Problem computing a Cauchy principle value

complex integral and singularity

Should $p.v.\int_0^1 x\cot(\pi x)dx$ converge?

An explanation or hints to evaluate $\text{PV}\int_0^\infty \frac{e^{-x}(x+\log (x))}{1-e^{-x}}dx$

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