DLMF:2.7.E23 (Q917)

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DLMF:2.7.E23
No description defined

    Statements

    Defining formula
    | ϵ j ⁢ ( x ) | , 1 2 ⁢ f - 1 / 2 ⁢ ( x ) ⁢ | ϵ j ′ ⁢ ( x ) | ≤ exp ⁡ ( 1 2 ⁢ 𝒱 a j , x ⁡ ( F ) ) - 1 , subscript italic-ϵ 𝑗 𝑥 1 2 superscript 𝑓 1 2 𝑥 superscript subscript italic-ϵ 𝑗 ′ 𝑥 1 2 variational-operator-on-interval subscript 𝑎 𝑗 𝑥 𝐹 1 {\displaystyle{\displaystyle|\epsilon_{j}(x)|,\;\;\tfrac{1}{2}f^{-1/2}(x)|% \epsilon_{j}^{\prime}(x)|\leq\exp\left(\tfrac{1}{2}\mathcal{V}_{a_{j},x}\left(% F\right)\right)-1,}}
    0 references
    DLMF id
    DLMF:2.7.E23
    0 references
    constraint
    j = 1 , 2 𝑗 1 2 {\displaystyle{\displaystyle j=1,2}}
    0 references
    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    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.m2adec
    0 references
    Q11060
    Defining formula
    ( a 1 , a 2 ) subscript 𝑎 1 subscript 𝑎 2 {\displaystyle{\displaystyle(a_{1},a_{2})}}
    xml-id
    C2.S7.XMD19.m1dec
    0 references
    Q11059
    Defining formula
    ϵ j ⁢ ( x ) subscript italic-ϵ 𝑗 𝑥 {\displaystyle{\displaystyle\epsilon_{j}(x)}}
    xml-id
    C2.S7.XMD22.m1bdec
    0 references
    Q11061
    Defining formula
    F 𝐹 {\displaystyle{\displaystyle F}}
    xml-id
    C2.S7.XMD23.m1dec
    0 references
     
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