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2.3.E6 - MaRDI portal

2.3.E6 (Q692)

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2.3.E6
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    Statements

    DLMF defining formula
    𝒱 a , b ⁡ ( f ⁢ ( t ) ) = ∫ a b | f ′ ⁢ ( t ) ⁢ d t | ; variational-operator-on-interval 𝑎 𝑏 𝑓 𝑡 superscript subscript 𝑎 𝑏 superscript 𝑓 ′ 𝑡 𝑡 {\displaystyle{\displaystyle\mathcal{V}_{a,b}\left(f(t)\right)=\int_{a}^{b}|f^% {\prime}(t)\mathrm{d}t|;}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    total variation
    DLMF 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.m2adec
    0 references
    left endpoint
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S3.XMD4.m1bdec
    0 references
    right endpoint
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S3.XMD5.m1adec
    0 references
     
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