DLMF:24.14.E11 (Q7556)

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DLMF:24.14.E11
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    Statements

    Defining formula
    det ⁡ [ B r + s ] = ( - 1 ) n ⁢ ( n + 1 ) / 2 ⁢ ( ∏ k = 1 n k ! ) 6 / ( ∏ k = 1 2 ⁢ n + 1 k ! ) , delimited-[] Bernoulli-number-B 𝑟 𝑠 superscript 1 𝑛 𝑛 1 2 superscript superscript subscript product 𝑘 1 𝑛 𝑘 6 superscript subscript product 𝑘 1 2 𝑛 1 𝑘 {\displaystyle{\displaystyle\det[B_{r+s}]=(-1)^{n(n+1)/2}\left(\prod_{k=1}^{n}% k!\right)^{6}\Bigg{/}\left(\prod_{k=1}^{2n+1}k!\right),}}
    0 references
    DLMF id
    DLMF:24.14.E11
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1afdec
    0 references
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1jdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1jdec
    0 references
    Q12127
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C24.S14.XMD1.m1dec
    0 references
    Q12128
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C24.S14.XMD2.m1dec
    0 references
     
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