DLMF:24.7.E11 (Q7487)

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DLMF:24.7.E11
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    Statements

    test
    B n ⁡ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ - c - i ⁢ ∞ - c + i ⁢ ∞ ( x + t ) n ⁢ ( π sin ⁡ ( π ⁢ t ) ) 2 ⁢ d t , Bernoulli-polynomial-B 𝑛 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 superscript 𝑥 𝑡 𝑛 superscript 𝜋 𝜋 𝑡 2 𝑡 {\displaystyle{\displaystyle B_{n}\left(x\right)=\frac{1}{2\pi i}\int_{-c-i% \infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin\left(\pi t\right)}\right)^{% 2}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:24.7.E11
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    constraint
    0 < c < 1 0 𝑐 1 {\displaystyle{\displaystyle 0<c<1}}
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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.m2abdec
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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.m2ajdec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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