Cauchy principal value, finite interval

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-12.26

https://metanorma.github.io/isq-smart/math/part-2-12/t2-12.26
urn:iso:std:iso:80000:-2:ed-2:en:item:2-12.26

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-12.26

IEC

urn:iec:std:iec:80000-2:2019:::item:2-12.26

Designations

ENCauchy principal value, finite interval

FRvaleur principale de Cauchy, intervalle fini

Symbol

⨍_{a}^{b} f (x) d x

Notation systems

AsciiMath

⨍_a^b f(x)"d"x

LaTeX

⨍_{a}^{b} f ( x ) \text{d} x

Definition

Cauchy principal value of the integral of $f$ with singularity at $c$ , where $a < c < b$

valeur principale de Cauchy de l'intégrale d'une fonction $f$ non définie en $c$ , où $a < c < b$

$lim_{δ \to 0 +} (\int_{a}^{c - δ} f (x) d x + \int_{c + δ}^{b} f (x) d x)$

A mathematical concept as defined in ISO/IEC 80000 Part 2.

isq:t2-12.26

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-12.26
skosxl:prefLabel	"Cauchy principal value, finite interval"@en
skosxl:altLabel	"⨍_a^b f(x)"d"x"@en
skos:definition	Cauchy principal value of the integral of stem:[f] with singularity at stem:[c], where stem:[a<c<b]
skos:note	stem:[lim_(delta -> 0+) (int_a^(c-delta)f(x)"d"x + int_(c+delta)^b f(x)"d"x)]
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-12