DLMF:24.13.E4 (Q7538)

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DLMF:24.13.E4
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    Defining formula
    ∫ 0 1 / 2 B n ⁡ ( t ) ⁢ d t = 1 - 2 n + 1 2 n ⁢ B n + 1 n + 1 , superscript subscript 0 1 2 Bernoulli-polynomial-B 𝑛 𝑡 𝑡 1 superscript 2 𝑛 1 superscript 2 𝑛 Bernoulli-number-B 𝑛 1 𝑛 1 {\displaystyle{\displaystyle\int_{0}^{1/2}B_{n}\left(t\right)\mathrm{d}t=\frac% {1-2^{n+1}}{2^{n}}\frac{B_{n+1}}{n+1},}}
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    DLMF:24.13.E4
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