DLMF:24.16.E8 (Q7578): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1adec

Revision as of 00:50, 2 January 2020

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DLMF:24.16.E8
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    Statements

    test
    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
    0 references
    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    0 references
     
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