DLMF:4.10.E5 (Q1620)

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DLMF:4.10.E5
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    Statements

    Defining formula
    ∫ 0 1 ln ⁡ t 1 - t ⁢ d t = - π 2 6 , superscript subscript 0 1 𝑡 1 𝑡 𝑡 superscript 𝜋 2 6 {\displaystyle{\displaystyle\int_{0}^{1}\frac{\ln t}{1-t}\mathrm{d}t=-\frac{% \pi^{2}}{6},}}
    0 references
    DLMF id
    DLMF:4.10.E5
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
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