DLMF:25.12.E5 (Q7724): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.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.m2addec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12150 / qualifier
 
xml-id: C25.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12151 / rank
 
Normal rank
Property / Symbols used: Q12151 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12151 / qualifier
 
xml-id: C25.S1.XMD2.m1dec
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.m1ddec

Latest revision as of 12:48, 2 January 2020

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English
DLMF:25.12.E5
No description defined

    Statements

    test
    Li 2 ⁡ ( z m ) = m ⁢ ∑ k = 0 m - 1 Li 2 ⁡ ( z ⁢ e 2 ⁢ π ⁢ i ⁢ k / m ) , dilogarithm superscript 𝑧 𝑚 𝑚 superscript subscript 𝑘 0 𝑚 1 dilogarithm 𝑧 superscript 𝑒 2 𝜋 𝑖 𝑘 𝑚 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(z^{m}\right)=m\sum_{k=0}^{m-1% }\mathrm{Li}_{2}\left(ze^{2\pi ik/m}\right),}}
    0 references
    DLMF id
    DLMF:25.12.E5
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    dilogarithm
    test
    Li 2 ⁡ ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12150
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1dec
    0 references
    Q12151
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1dec
    0 references
    Q12156
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C25.S1.XMD8.m1ddec
    0 references
     
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