DLMF:25.12.E7 (Q7726): Difference between revisions

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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.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q12167 / rank
 
Normal rank
Property / Symbols used: Q12167 / qualifier
 
test:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q12167 / qualifier
 
xml-id: C25.S12.XMD1.m1dec

Latest revision as of 12:48, 2 January 2020

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English
DLMF:25.12.E7
No description defined

    Statements

    Li 2 ( e i θ ) = n = 1 cos ( n θ ) n 2 + i n = 1 sin ( n θ ) n 2 . dilogarithm superscript 𝑒 𝑖 𝜃 superscript subscript 𝑛 1 𝑛 𝜃 superscript 𝑛 2 𝑖 superscript subscript 𝑛 1 𝑛 𝜃 superscript 𝑛 2 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(e^{i\theta}\right)=\sum_{n=1}% ^{\infty}\frac{\cos\left(n\theta\right)}{n^{2}}+i\sum_{n=1}^{\infty}\frac{\sin% \left(n\theta\right)}{n^{2}}.}}
    0 references
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    Li 2 ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    C25.S12.E1.m2afdec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1adec
    0 references
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    C25.S12.XMD1.m1dec
    0 references