DLMF:1.4.E25 (Q104)

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DLMF:1.4.E25
No description defined

    Statements

    Defining formula
    ⨍ - ∞ ∞ f ⁢ ( x ) ⁢ d x = P ⁢ ∫ - ∞ ∞ f ⁢ ( x ) ⁢ d x = lim b → ∞ ⁡ ∫ - b b f ⁢ ( x ) ⁢ d x , subscript superscript principal-value-integral 𝑓 𝑥 𝑥 𝑃 subscript superscript 𝑓 𝑥 𝑥 subscript → 𝑏 subscript superscript 𝑏 𝑏 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\pvint^{\infty}_{-\infty}f(x)\mathrm{d}x=P\int^{% \infty}_{-\infty}f(x)\mathrm{d}x=\lim_{b\to\infty}\int^{b}_{-b}f(x)\mathrm{d}x% ,}}
    0 references
    DLMF id
    DLMF:1.4.E25
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
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    Cauchy principal value
    Defining formula
    ⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    xml-id
    C1.S4.E24.m2aadec
    0 references
     
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