DLMF:25.6.E18 (Q7655)

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DLMF:25.6.E18
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    Statements

    Defining formula
    ( n + 1 4 ) ⁢ ζ ⁡ ( 4 ⁢ n ) + 1 2 ⁢ ( ζ ⁡ ( 2 ⁢ n ) ) 2 = ∑ k = 1 n ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 4 ⁢ n - 2 ⁢ k ) , 𝑛 1 4 Riemann-zeta 4 𝑛 1 2 superscript Riemann-zeta 2 𝑛 2 superscript subscript 𝑘 1 𝑛 Riemann-zeta 2 𝑘 Riemann-zeta 4 𝑛 2 𝑘 {\displaystyle{\displaystyle{\left(n+\tfrac{1}{4}\right)\zeta\left(4n\right)+% \tfrac{1}{2}(\zeta\left(2n\right))^{2}=\sum_{k=1}^{n}\zeta\left(2k\right)\zeta% \left(4n-2k\right)},}}
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    DLMF id
    DLMF:25.6.E18
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    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
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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.m2aqdec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1idec
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