DLMF:1.4.E34 (Q113)

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DLMF:1.4.E34
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    Statements

    Defining formula
    𝒱 a , b ⁡ ( f ) = ∫ a b | f ′ ⁢ ( x ) ⁢ d x | , variational-operator-on-interval 𝑎 𝑏 𝑓 subscript superscript 𝑏 𝑎 superscript 𝑓 ′ 𝑥 𝑥 {\displaystyle{\displaystyle\mathcal{V}_{a,b}\left(f\right)=\int^{b}_{a}|f^{% \prime}(x)\mathrm{d}x|,}}
    0 references
    DLMF id
    DLMF:1.4.E34
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
    0 references
    total variation
    Defining formula
    𝒱 a , b ⁡ ( f ) variational-operator-on-interval 𝑎 𝑏 𝑓 {\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}}
    xml-id
    C1.S4.E33.m2aadec
    0 references
     
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