DLMF:24.14.E7 (Q7552)

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DLMF:24.14.E7
No description defined

    Statements

    Defining formula
    ∑ j = 0 m ∑ k = 0 n ( m j ) ⁢ ( n k ) ⁢ B j ⁢ B k m + n - j - k + 1 = ( - 1 ) m - 1 ⁢ m ! ⁢ n ! ( m + n ) ! ⁢ B m + n . superscript subscript 𝑗 0 𝑚 superscript subscript 𝑘 0 𝑛 binomial 𝑚 𝑗 binomial 𝑛 𝑘 Bernoulli-number-B 𝑗 Bernoulli-number-B 𝑘 𝑚 𝑛 𝑗 𝑘 1 superscript 1 𝑚 1 𝑚 𝑛 𝑚 𝑛 Bernoulli-number-B 𝑚 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{m}\sum_{k=0}^{n}\genfrac{(}{)}{0.0pt}{% }{m}{j}\genfrac{(}{)}{0.0pt}{}{n}{k}\frac{B_{j}B_{k}}{m+n-j-k+1}=(-1)^{m-1}% \frac{m!n!}{(m+n)!}B_{m+n}.}}
    0 references
    DLMF id
    DLMF:24.14.E7
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1afdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1dec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1fdec
    0 references
    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1dec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1fdec
    0 references
     
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