DLMF:25.12.E3 (Q7722): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11243 / rank
 
Normal rank
Property / Symbols used: Q11243 / qualifier
 
test:

[ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}

[\NVar{a},\NVar{b})
Property / Symbols used: Q11243 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r1.m4adec
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
test:

{\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2aadec
Property / Symbols used
 
Property / Symbols used: dilogarithm / rank
 
Normal rank
Property / Symbols used: dilogarithm / qualifier
 
test:

Li 2 ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}

\dilog@{\NVar{z}}
Property / Symbols used: dilogarithm / qualifier
 
xml-id: C25.S12.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

{\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10785 / rank
 
Normal rank
Property / Symbols used: Q10785 / qualifier
 
test:

{\displaystyle{\displaystyle\setminus}}

\setminus
Property / Symbols used: Q10785 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r19.m2aadec
Property / Symbols used
 
Property / Symbols used: Q12152 / rank
 
Normal rank
Property / Symbols used: Q12152 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12152 / qualifier
 
xml-id: C25.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12156 / rank
 
Normal rank
Property / Symbols used: Q12156 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12156 / qualifier
 
xml-id: C25.S1.XMD8.m1bdec

Latest revision as of 12:47, 2 January 2020

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DLMF:25.12.E3
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    Statements

    Li 2 ( z ) + Li 2 ( z z - 1 ) = - 1 2 ( ln ( 1 - z ) ) 2 , dilogarithm 𝑧 dilogarithm 𝑧 𝑧 1 1 2 superscript 1 𝑧 2 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(z\right)+\mathrm{Li}_{2}\left% (\frac{z}{z-1}\right)=-\frac{1}{2}(\ln\left(1-z\right))^{2},}}
    0 references
    0 references
    z [ 1 , ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus[1,\infty)}}
    0 references
    [ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}
    introduction.Sx4.p2.t1.r1.m4adec
    0 references
    {\displaystyle{\displaystyle\mathbb{C}}}
    introduction.Sx4.p1.t1.r1.m2aadec
    0 references
    Li 2 ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    C25.S12.E1.m2abdec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    {\displaystyle{\displaystyle\setminus}}
    introduction.Sx4.p2.t1.r19.m2aadec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C25.S1.XMD5.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C25.S1.XMD8.m1bdec
    0 references