DLMF:5.20.E4 (Q2209)

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DLMF:5.20.E4
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    Statements

    Defining formula
    W = - ∑ 1 ≤ ℓ < j ≤ n ln ⁡ | e i ⁢ θ ℓ - e i ⁢ θ j | , 𝑊 subscript 1 ℓ 𝑗 𝑛 superscript 𝑒 𝑖 subscript 𝜃 ℓ superscript 𝑒 𝑖 subscript 𝜃 𝑗 {\displaystyle{\displaystyle W=-\sum_{1\leq\ell<j\leq n}\ln|e^{i\theta_{\ell}}% -e^{i\theta_{j}}|,}}
    0 references
    DLMF id
    DLMF:5.20.E4
    0 references
    Symbols used
    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.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11292
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C5.S1.XMD1.m1bdec
    0 references
    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1cdec
    0 references
    Q11300
    Defining formula
    W 𝑊 {\displaystyle{\displaystyle W}}
    xml-id
    C5.S20.XMD1.m1cdec
    0 references
     
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