DLMF:24.7.E4 (Q7480)

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DLMF:24.7.E4
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    Statements

    Defining formula
    B 2 ⁢ n = ( - 1 ) n + 1 ⁢ π ⁢ ∫ 0 ∞ t 2 ⁢ n ⁢ csch 2 ⁡ ( π ⁢ t ) ⁢ d t , Bernoulli-number-B 2 𝑛 superscript 1 𝑛 1 𝜋 superscript subscript 0 superscript 𝑡 2 𝑛 2 𝜋 𝑡 𝑡 {\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}{% \operatorname{csch}^{2}}\left(\pi t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:24.7.E4
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    hyperbolic cosecant function
    Defining formula
    csch ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}
    xml-id
    C4.S28.E5.m2aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1cdec
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