DLMF:24.7.E11 (Q7487)

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DLMF:24.7.E11
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    Statements

    Defining formula
    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,}}
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    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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