Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Sokhotski–Plemelj_theorem
|
| gptkbp:describes |
behavior of Cauchy principal value integrals
|
| gptkbp:expressedIn |
limit of integrals involving simple poles
|
| gptkbp:field |
complex analysis
|
| gptkbp:form |
\\lim_{\\epsilon \\to 0^+} \\int_{-\\infty}^{\\infty} \\frac{f(x)}{x \\pm i\\epsilon} dx = \\mathcal{P} \\int_{-\\infty}^{\\infty} \\frac{f(x)}{x} dx \\mp i\\pi f(0)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sokhotski formula
|
| gptkbp:namedAfter |
gptkb:Yulian_Sokhotski
|
| gptkbp:publishedIn |
1873
|
| gptkbp:relatedTo |
gptkb:Hilbert_transform
gptkb:Cauchy_integral_formula |
| gptkbp:usedIn |
gptkb:quantum_field_theory
mathematical physics theory of distributions |
| gptkbp:bfsParent |
gptkb:Sokhotski–Plemelj_theorem
|
| gptkbp:bfsLayer |
7
|