DLMF:24.16.E4 (Q8267)

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DLMF:24.16.E4
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    Statements

    DLMF defining formula
    ( ln ⁡ ( 1 + t ) t ) ℓ = ℓ ⁢ ∑ n = 0 ∞ B n ( ℓ + n ) ℓ + n ⁢ t n n ! , superscript 1 𝑡 𝑡 ℓ ℓ superscript subscript 𝑛 0 generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑛 ℓ 𝑛 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\left(\frac{\ln\left(1+t\right)}{t}\right)^{\ell}=% \ell\sum_{n=0}^{\infty}\frac{B^{(\ell+n)}_{n}}{\ell+n}\frac{t^{n}}{n!},}}
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    constraint
    | t | < 1 𝑡 1 {\displaystyle{\displaystyle|t|<1}}
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    Symbols used
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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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.m3abdec
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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C24.S1.XMD3.m1cdec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
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    real or complex
    DLMF defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1bdec
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    Identifiers

     
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