DLMF:24.16.E8 (Q7578)

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DLMF:24.16.E8
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    Statements

    Defining formula
    β n ⁢ ( λ ) = n ! ⁢ b n ⁢ λ n + ∑ k = 1 ⌊ n / 2 ⌋ n 2 ⁢ k ⁢ B 2 ⁢ k ⁢ s ⁡ ( n - 1 , 2 ⁢ k - 1 ) ⁢ λ n - 2 ⁢ k , subscript 𝛽 𝑛 𝜆 𝑛 subscript 𝑏 𝑛 superscript 𝜆 𝑛 superscript subscript 𝑘 1 𝑛 2 𝑛 2 𝑘 Bernoulli-number-B 2 𝑘 Stirling-number-first-kind-S 𝑛 1 2 𝑘 1 superscript 𝜆 𝑛 2 𝑘 {\displaystyle{\displaystyle\beta_{n}(\lambda)=n!b_{n}\lambda^{n}+\sum_{k=1}^{% \left\lfloor\ifrac{n}{2}\right\rfloor}\frac{n}{2k}B_{2k}s\left(n-1,2k-1\right)% \lambda^{n-2k},}}
    0 references
    DLMF id
    DLMF:24.16.E8
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    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
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    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
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    Q12137
    Defining formula
    β n ⁢ ( λ ) subscript 𝛽 𝑛 𝜆 {\displaystyle{\displaystyle\beta_{n}(\lambda)}}
    xml-id
    C24.S16.XMD2.m1adec
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