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DLMF:24.8.E7 - MaRDI portal

DLMF:24.8.E7 (Q8187)

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DLMF:24.8.E7
No description defined

    Statements

    DLMF defining formula
    B 2 ⁢ n = ( - 1 ) n + 1 ⁢ 4 ⁢ n 2 2 ⁢ n - 1 ⁢ ∑ k = 1 ∞ k 2 ⁢ n - 1 e π ⁢ k + ( - 1 ) k + n , Bernoulli-number-B 2 𝑛 superscript 1 𝑛 1 4 𝑛 superscript 2 2 𝑛 1 superscript subscript 𝑘 1 superscript 𝑘 2 𝑛 1 superscript 𝑒 𝜋 𝑘 superscript 1 𝑘 𝑛 {\displaystyle{\displaystyle B_{2n}=\frac{(-1)^{n+1}4n}{2^{2n}-1}\sum_{k=1}^{% \infty}\frac{k^{2n-1}}{e^{\pi k}+(-1)^{k+n}},}}
    0 references
    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
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    Symbols used
    Q11083
    DLMF defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1fdec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1fdec
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    Identifiers

     
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