DLMF:24.8.E3 (Q7490)

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DLMF:24.8.E3
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    Defining formula
    B n ⁡ ( x ) = - n ! ( 2 ⁢ π ⁢ i ) n ⁢ ∑ k = - ∞ k ≠ 0 ∞ e 2 ⁢ π ⁢ i ⁢ k ⁢ x k n . Bernoulli-polynomial-B 𝑛 𝑥 𝑛 superscript 2 𝜋 𝑖 𝑛 superscript subscript 𝑘 𝑘 0 superscript 𝑒 2 𝜋 𝑖 𝑘 𝑥 superscript 𝑘 𝑛 {\displaystyle{\displaystyle B_{n}\left(x\right)=-\frac{n!}{(2\pi i)^{n}}\sum_% {\begin{subarray}{c}k=-\infty\\ k\neq 0\end{subarray}}^{\infty}\frac{e^{2\pi ikx}}{k^{n}}.}}
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    DLMF:24.8.E3
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