DLMF:25.12.E5 (Q7724)

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DLMF:25.12.E5
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    Statements

    Defining formula
    Li 2 ⁡ ( z m ) = m ⁢ ∑ k = 0 m - 1 Li 2 ⁡ ( z ⁢ e 2 ⁢ π ⁢ i ⁢ k / m ) , dilogarithm superscript 𝑧 𝑚 𝑚 superscript subscript 𝑘 0 𝑚 1 dilogarithm 𝑧 superscript 𝑒 2 𝜋 𝑖 𝑘 𝑚 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(z^{m}\right)=m\sum_{k=0}^{m-1% }\mathrm{Li}_{2}\left(ze^{2\pi ik/m}\right),}}
    0 references
    DLMF id
    DLMF:25.12.E5
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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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.m2aadec
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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.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1dec
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    Q12151
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1dec
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    Q12156
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1ddec
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