DLMF:1.4.E24 (Q103)

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DLMF:1.4.E24
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    Statements

    test
    ⨍ 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 ) , subscript superscript principal-value-integral 𝑏 𝑎 𝑓 𝑥 𝑥 𝑃 subscript superscript 𝑏 𝑎 𝑓 𝑥 𝑥 subscript → italic-ϵ limit-from 0 subscript superscript 𝑐 italic-ϵ 𝑎 𝑓 𝑥 𝑥 subscript superscript 𝑏 𝑐 italic-ϵ 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\pvint^{b}_{a}f(x)\mathrm{d}x=P\int^{b}_{a}f(x)% \mathrm{d}x=\lim_{\epsilon\to 0+}\left(\int^{c-\epsilon}_{a}f(x)\mathrm{d}x+% \int^{b}_{c+\epsilon}f(x)\mathrm{d}x\right),}}
    0 references
    DLMF id
    DLMF:1.4.E24
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
     
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