DLMF:25.6.E16 (Q7653)

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DLMF:25.6.E16
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    Statements

    Defining formula
    ( n + 1 2 ) ⁢ ζ ⁡ ( 2 ⁢ n ) = ∑ k = 1 n - 1 ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ n - 2 ⁢ k ) , 𝑛 1 2 Riemann-zeta 2 𝑛 superscript subscript 𝑘 1 𝑛 1 Riemann-zeta 2 𝑘 Riemann-zeta 2 𝑛 2 𝑘 {\displaystyle{\displaystyle\left(n+\tfrac{1}{2}\right)\zeta\left(2n\right)=% \sum_{k=1}^{n-1}\zeta\left(2k\right)\zeta\left(2n-2k\right),}}
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    DLMF id
    DLMF:25.6.E16
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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.m2aodec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1gdec
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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1gdec
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