DLMF:25.12.E6 (Q7725): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12152 / rank
 
Normal rank
Property / Symbols used: Q12152 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12152 / qualifier
 
xml-id: C25.S1.XMD5.m1cdec

Latest revision as of 13:48, 2 January 2020

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DLMF:25.12.E6
No description defined

    Statements

    Defining formula
    Li 2 ⁡ ( x ) + Li 2 ⁡ ( 1 - x ) = 1 6 ⁢ π 2 - ( ln ⁡ x ) ⁢ ln ⁡ ( 1 - x ) , dilogarithm 𝑥 dilogarithm 1 𝑥 1 6 superscript 𝜋 2 𝑥 1 𝑥 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(x\right)+\mathrm{Li}_{2}\left% (1-x\right)=\frac{1}{6}\pi^{2}-(\ln x)\ln\left(1-x\right),}}
    0 references
    DLMF id
    DLMF:25.12.E6
    0 references
    constraint
    0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<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.m2abdec
    0 references
    dilogarithm
    Defining formula
    Li 2 ⁡ ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E1.m2aedec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q12152
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C25.S1.XMD5.m1cdec
    0 references
     
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