DLMF:23.8.E5 (Q7287)

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DLMF:23.8.E5
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    Statements

    Defining formula
    η 1 = π 2 2 ⁢ ω 1 ⁢ ( 1 6 + ∑ n = 1 ∞ csc 2 ⁡ ( n ⁢ π ⁢ ω 3 ω 1 ) ) , subscript 𝜂 1 superscript 𝜋 2 2 subscript 𝜔 1 1 6 superscript subscript 𝑛 1 2 𝑛 𝜋 subscript 𝜔 3 subscript 𝜔 1 {\displaystyle{\displaystyle\eta_{1}=\frac{\pi^{2}}{2\omega_{1}}\left(\frac{1}% {6}+\sum_{n=1}^{\infty}{\csc^{2}}\left(\frac{n\pi\omega_{3}}{\omega_{1}}\right% )\right),}}
    0 references
    DLMF id
    DLMF:23.8.E5
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    cosecant function
    Defining formula
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2abdec
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    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1ddec
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    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1ddec
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    Q12072
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S8.XMD1.m1bdec
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