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

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec
Property / Symbols used
 
Property / Symbols used: dilogarithm / rank
 
Normal rank
Property / Symbols used: dilogarithm / qualifier
 
Defining formula:

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.m2afdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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
 
Defining formula:

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
 
Defining formula:

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
 
Defining formula:

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

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

Latest revision as of 13:48, 2 January 2020

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DLMF:25.12.E7
No description defined

    Statements

    Defining formula
    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
    DLMF id
    DLMF:25.12.E7
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    dilogarithm
    Defining formula
    Li 2 ⁡ ( z ) dilogarithm 𝑧 {\displaystyle{\displaystyle\mathrm{Li}_{2}\left(\NVar{z}\right)}}
    xml-id
    C25.S12.E1.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1adec
    0 references
    Q12167
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C25.S12.XMD1.m1dec
    0 references
     
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