DLMF:24.7.E5 (Q7481)

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DLMF:24.7.E5
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    Statements

    Defining formula
    B 2 ⁢ n = ( - 1 ) n ⁢ 2 ⁢ n ⁢ ( 2 ⁢ n - 1 ) π ⁢ ∫ 0 ∞ t 2 ⁢ n - 2 ⁢ ln ⁡ ( 1 - e - 2 ⁢ π ⁢ t ) ⁢ d t . Bernoulli-number-B 2 𝑛 superscript 1 𝑛 2 𝑛 2 𝑛 1 𝜋 superscript subscript 0 superscript 𝑡 2 𝑛 2 1 superscript 𝑒 2 𝜋 𝑡 𝑡 {\displaystyle{\displaystyle B_{2n}=(-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{% \infty}t^{2n-2}\ln\left(1-e^{-2\pi t}\right)\mathrm{d}t.}}
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    DLMF id
    DLMF:24.7.E5
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
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    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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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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