DLMF:24.7.E8 (Q7484)

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DLMF:24.7.E8
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    Statements

    test
    B 2 ⁢ n + 1 ⁡ ( x ) = ( - 1 ) n + 1 ⁢ ( 2 ⁢ n + 1 ) ⁢ ∫ 0 ∞ sin ⁡ ( 2 ⁢ π ⁢ x ) cosh ⁡ ( 2 ⁢ π ⁢ t ) - cos ⁡ ( 2 ⁢ π ⁢ x ) ⁢ t 2 ⁢ n ⁢ d t . Bernoulli-polynomial-B 2 𝑛 1 𝑥 superscript 1 𝑛 1 2 𝑛 1 superscript subscript 0 2 𝜋 𝑥 2 𝜋 𝑡 2 𝜋 𝑥 superscript 𝑡 2 𝑛 𝑡 {\displaystyle{\displaystyle B_{2n+1}\left(x\right)=(-1)^{n+1}(2n+1)\*\int_{0}% ^{\infty}\frac{\sin\left(2\pi x\right)}{\cosh\left(2\pi t\right)-\cos\left(2% \pi x\right)}t^{2n}\mathrm{d}t.}}
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    DLMF id
    DLMF:24.7.E8
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    Symbols used
    Q11288
    test
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2aadec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    hyperbolic cosine function
    test
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aadec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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