DLMF:25.14.E3 (Q7742)

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DLMF:25.14.E3
No description defined

    Statements

    Defining formula
    Li s ⁑ ( z ) = z ⁒ Ξ¦ ⁑ ( z , s , 1 ) , polylogarithm 𝑠 𝑧 𝑧 Lerch-Phi 𝑧 𝑠 1 {\displaystyle{\displaystyle\mathrm{Li}_{s}\left(z\right)=z\Phi\left(z,s,1% \right),}}
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    DLMF id
    DLMF:25.14.E3
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    constraint
    β„œ ⁑ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    β„œ ⁑ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    | z | ≀ 1 𝑧 1 {\displaystyle{\displaystyle|z|\leq 1}}
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    Symbols used
    Lerch’s transcendent
    Defining formula
    Ξ¦ ⁑ ( z , s , a ) Lerch-Phi 𝑧 𝑠 π‘Ž {\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S14.E1.m2abdec
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    polylogarithm
    Defining formula
    Li s ⁑ ( z ) polylogarithm 𝑠 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E10.m2adec
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    Q10811
    Defining formula
    β„œ ⁑ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
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    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1bdec
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    Q12156
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1adec
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