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DLMF:25.6.E19 - MaRDI portal

DLMF:25.6.E19 (Q8349)

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DLMF:25.6.E19
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    Statements

    DLMF defining formula
    ( m + n + 3 2 ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 ) = ( ∑ k = 1 m + ∑ k = 1 n ) ⁢ ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 - 2 ⁢ k ) , 𝑚 𝑛 3 2 Riemann-zeta 2 𝑚 2 𝑛 2 superscript subscript 𝑘 1 𝑚 superscript subscript 𝑘 1 𝑛 Riemann-zeta 2 𝑘 Riemann-zeta 2 𝑚 2 𝑛 2 2 𝑘 {\displaystyle{\displaystyle\left(m+n+\tfrac{3}{2}\right)\zeta\left(2m+2n+2% \right)=\left(\sum_{k=1}^{m}+\sum_{k=1}^{n}\right)\zeta\left(2k\right)\zeta% \left(2m+2n+2-2k\right),}}
    0 references
    constraint
    m + n ≥ 1 𝑚 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}}
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    Symbols used
    Riemann zeta function
    DLMF defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ardec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1jdec
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    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1bdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1jdec
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    Identifiers

     
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