DLMF:24.16.E9 (Q8272)

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DLMF:24.16.E9
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    Statements

    DLMF defining formula
    ( t e t - 1 ) x = ∑ n = 0 ∞ B n ( x ) ⁢ t n n ! , superscript 𝑡 superscript 𝑒 𝑡 1 𝑥 superscript subscript 𝑛 0 generalized-Bernoulli-polynomial-B 𝑥 𝑛 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\left(\frac{t}{e^{t}-1}\right)^{x}=\sum_{n=0}^{% \infty}B^{(x)}_{n}\frac{t^{n}}{n!},}}
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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
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
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    generalized Bernoulli polynomials
    DLMF 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.m3addec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1hdec
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    real or complex
    DLMF defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1edec
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    real or complex
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1bdec
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    Identifiers

     
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