DLMF:25.6.E20 (Q7657)

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DLMF:25.6.E20
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    Statements

    Defining formula
    1 2 ⁢ ( 2 2 ⁢ n - 1 ) ⁢ ζ ⁡ ( 2 ⁢ n ) = ∑ k = 1 n - 1 ( 2 2 ⁢ n - 2 ⁢ k - 1 ) ⁢ ζ ⁡ ( 2 ⁢ n - 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ k ) , 1 2 superscript 2 2 𝑛 1 Riemann-zeta 2 𝑛 superscript subscript 𝑘 1 𝑛 1 superscript 2 2 𝑛 2 𝑘 1 Riemann-zeta 2 𝑛 2 𝑘 Riemann-zeta 2 𝑘 {\displaystyle{\displaystyle\tfrac{1}{2}(2^{2n}-1)\zeta\left(2n\right)=\sum_{k% =1}^{n-1}(2^{2n-2k}-1)\zeta\left(2n-2k\right)\zeta\left(2k\right),}}
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    DLMF id
    DLMF:25.6.E20
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    constraint
    n ≥ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}}
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    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2asdec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1kdec
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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1kdec
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