DLMF:24.15.E6 (Q7563)

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DLMF:24.15.E6
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    Statements

    Defining formula
    B n = ∑ k = 0 n ( - 1 ) k ⁢ k ! ⁢ S ⁡ ( n , k ) k + 1 , Bernoulli-number-B 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 𝑘 Stirling-number-second-kind-S 𝑛 𝑘 𝑘 1 {\displaystyle{\displaystyle B_{n}=\sum_{k=0}^{n}(-1)^{k}\frac{k!S\left(n,k% \right)}{k+1},}}
    0 references
    DLMF id
    DLMF:24.15.E6
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    Q12131
    Defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2adec
    0 references
     
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