DLMF:25.6.E2 (Q7639)

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DLMF:25.6.E2
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    Statements

    test
    ζ ⁡ ( 2 ⁢ n ) = ( 2 ⁢ π ) 2 ⁢ n 2 ⁢ ( 2 ⁢ n ) ! ⁢ | B 2 ⁢ n | , Riemann-zeta 2 𝑛 superscript 2 𝜋 2 𝑛 2 2 𝑛 Bernoulli-number-B 2 𝑛 {\displaystyle{\displaystyle\zeta\left(2n\right)=\frac{(2\pi)^{2n}}{2(2n)!}% \left|B_{2n}\right|,}}
    0 references
    DLMF id
    DLMF:25.6.E2
    0 references
    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
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    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
     
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