DLMF:24.13.E4 (Q7538)

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DLMF:24.13.E4
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    Statements

    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},}}
    0 references
    DLMF id
    DLMF:24.13.E4
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    0 references
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1cdec
    0 references
     
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