DLMF:24.13.E3 (Q7537)

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DLMF:24.13.E3
No description defined

    Statements

    Defining formula
    ∫ x x + ( 1 / 2 ) B n ⁡ ( t ) ⁢ d t = E n ⁡ ( 2 ⁢ x ) 2 n + 1 , superscript subscript 𝑥 𝑥 1 2 Bernoulli-polynomial-B 𝑛 𝑡 𝑡 Euler-polynomial-E 𝑛 2 𝑥 superscript 2 𝑛 1 {\displaystyle{\displaystyle\int_{x}^{x+(1/2)}B_{n}\left(t\right)\mathrm{d}t=% \frac{E_{n}\left(2x\right)}{2^{n+1}},}}
    0 references
    DLMF id
    DLMF:24.13.E3
    0 references
    Symbols used
    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.m2abdec
    0 references
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1bdec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1bdec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1adec
    0 references
     
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