DLMF:1.7.E11 (Q252)

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DLMF:1.7.E11
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    Statements

    Defining formula
    exp ⁡ ( ∫ 0 1 ln ⁡ ( f ⁢ ( x ) ) ⁢ d x ) < ∫ 0 1 f ⁢ ( x ) ⁢ d x . subscript superscript 1 0 𝑓 𝑥 𝑥 subscript superscript 1 0 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\exp\left(\int^{1}_{0}\ln\left(f(x)\right)\mathrm{% d}x\right)<\int^{1}_{0}f(x)\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.7.E11
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
     
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