DLMF:24.16.E1 (Q7570)

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DLMF:24.16.E1
No description defined

    Statements

    Defining formula
    ( t e t - 1 ) ℓ ⁢ e x ⁢ t = ∑ n = 0 ∞ B n ( ℓ ) ⁡ ( x ) ⁢ t n n ! , superscript 𝑡 superscript 𝑒 𝑡 1 ℓ superscript 𝑒 𝑥 𝑡 superscript subscript 𝑛 0 generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑥 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\left(\frac{t}{e^{t}-1}\right)^{\ell}e^{xt}=\sum_{% n=0}^{\infty}B^{(\ell)}_{n}\left(x\right)\frac{t^{n}}{n!},}}
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    DLMF id
    DLMF:24.16.E1
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    constraint
    | t | < 2 ⁢ π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\pi}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11289
    Defining formula
    B n ( ℓ ) ⁡ ( x ) generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑥 {\displaystyle{\displaystyle B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S16.Px1.p1.m3adec
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    Q12122
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C24.S1.XMD3.m1dec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1dec
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    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1dec
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    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1dec
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