DLMF:1.4.E24
type: Item
Digital Library of Mathematical Functions ID: 1.4.E24
DLMF defining formula: ⨍ a b f ⁢ ( x ) ⁢ d x = P ⁢ ∫ a b f ⁢ ( x ) ⁢ d x = lim ϵ → 0 + ⁡ ( ∫ a c - ϵ f ⁢ ( x ) ⁢ d x + ∫ c + ϵ b f ⁢ ( x ) ⁢ d x ) , <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.42.2.cmml" xref="p1.1.m1.1.42"> <and id="p1.1.m1.1.42.2a.cmml" xref="p1.1.m1.1.42"/> <apply id="p1.1.m1.1.42.2b.cmml" xref="p1.1.m1.1.42"> <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/> <apply id="p1.1.m1.1.42.2.2.cmml" xref="p1.1.m1.1.42.2.2"> <apply id="p1.1.m1.1.42.2.2.1.cmml" xref="p1.1.m1.1.42.2.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.42.2.2.1.1.cmml" xref="p1.1.m1.1.42.2.2.1">subscript</csymbol> <apply id="p1.1.m1.1.42.2.2.1.2.cmml" xref="p1.1.m1.1.42.2.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.42.2.2.1.2.1.cmml" xref="p1.1.m1.1.42.2.2.1">superscript</csymbol> <csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">principal-value-integral</csymbol> <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑏</ci> </apply> <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">𝑎</ci> </apply> <apply id="p1.1.m1.1.42.2.2.2.cmml" xref="p1.1.m1.1.42.2.2.2"> <times id="p1.1.m1.1.42.2.2.2.1.cmml" xref="p1.1.m1.1.42.2.2.2.1"/> <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑓</ci> <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑥</ci> <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.2"> <diff id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.2.1.2"/> <ci id="p1.1.m1.1.8.2.2.cmml" xref="p1.1.m1.1.8.2.2">𝑥</ci> </apply> </apply> </apply> <apply id="p1.1.m1.1.42.2.3.cmml" xref="p1.1.m1.1.42.2.3"> <times id="p1.1.m1.1.42.2.3.1.cmml" xref="p1.1.m1.1.42.2.3.1"/> <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑃</ci> <apply id="p1.1.m1.1.42.2.3.2.cmml" xref="p1.1.m1.1.42.2.3.2"> <apply id="p1.1.m1.1.42.2.3.2.1.cmml" xref="p1.1.m1.1.42.2.3.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.42.2.3.2.1.1.cmml" xref="p1.1.m1.1.42.2.3.2.1">subscript</csymbol> <apply id="p1.1.m1.1.42.2.3.2.1.2.cmml" xref="p1.1.m1.1.42.2.3.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.42.2.3.2.1.2.1.cmml" xref="p1.1.m1…
Symbols defined: Cauchy principal value
Symbols used: differential of x
Symbols used: integral
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile