DLMF:25.14.E3 (Q7742): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec

Revision as of 01:02, 2 January 2020

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DLMF:25.14.E3
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    Statements

    Defining formula
    Li s ⁡ ( z ) = z ⁢ Φ ⁡ ( 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
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    ℜ ⁡ 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
    Φ ⁡ ( z , s , a ) Lerch-Phi 𝑧 𝑠 𝑎 {\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S14.E1.m2abdec
    0 references
    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
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
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