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

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Property / constraint
 

z ∈ ℂ ∖ [ 1 , ∞ ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus[1,\infty)}}

z\in\Complexes\setminus[1,\infty)
Property / constraint: z ∈ ℂ ∖ [ 1 , ∞ ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus[1,\infty)}} / rank
 
Normal rank
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:

ℂ {\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

No description defined
Language Label Description Also known as
English
DLMF:25.12.E3
No description defined

    Statements

    test
    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
    DLMF id
    DLMF:25.12.E3
    0 references
    constraint
    z ∈ ℂ ∖ [ 1 , ∞ ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus[1,\infty)}}
    0 references
    Symbols used
    Q11243
    test
    [ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p2.t1.r1.m4adec
    0 references
    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2aadec
    0 references
    dilogarithm
    test
    Li 2 ⁡ ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E1.m2abdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q10785
    test
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2aadec
    0 references
    Q12152
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C25.S1.XMD5.m1bdec
    0 references
    Q12156
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1bdec
    0 references
     
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