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DLMF:24.15.E7 - MaRDI portal

DLMF:24.15.E7 (Q8257)

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DLMF:24.15.E7
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    Statements

    DLMF defining formula
    B n = ∑ k = 0 n ( - 1 ) k ⁢ ( n + 1 k + 1 ) ⁢ S ⁡ ( n + k , k ) / ( n + k k ) , Bernoulli-number-B 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 binomial 𝑛 1 𝑘 1 Stirling-number-second-kind-S 𝑛 𝑘 𝑘 binomial 𝑛 𝑘 𝑘 {\displaystyle{\displaystyle B_{n}=\sum_{k=0}^{n}(-1)^{k}\genfrac{(}{)}{0.0pt}% {}{n+1}{k+1}S\left(n+k,k\right)\bigg{/}\genfrac{(}{)}{0.0pt}{}{n+k}{k},}}
    0 references
    Symbols used
    Q11083
    DLMF defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    Q12134
    DLMF 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.m2aadec
    0 references
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
    0 references

    Identifiers

     
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