DLMF:25.12.E4 (Q7723)

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DLMF:25.12.E4
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    Statements

    Defining formula
    Li 2 ⁡ ( z ) + Li 2 ⁡ ( 1 z ) = - 1 6 ⁢ π 2 - 1 2 ⁢ ( ln ⁡ ( - z ) ) 2 , dilogarithm 𝑧 dilogarithm 1 𝑧 1 6 superscript 𝜋 2 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(z\right)+\mathrm{Li}_{2}\left% (\frac{1}{z}\right)=-\frac{1}{6}\pi^{2}-\frac{1}{2}(\ln\left(-z\right))^{2},}}
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    DLMF id
    DLMF:25.12.E4
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    constraint
    z ∈ ℂ ∖ [ 0 , ∞ ) 𝑧 0 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus[0,\infty)}}
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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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    Q11243
    Defining formula
    [ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p2.t1.r1.m4aadec
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    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2abdec
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    dilogarithm
    Defining formula
    Li 2 ⁡ ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E1.m2acdec
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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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