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DLMF:25.6.E10 - MaRDI portal

DLMF:25.6.E10 (Q8340)

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DLMF:25.6.E10
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    Statements

    DLMF defining formula
    ζ ⁡ ( 4 ) = 36 17 ⁢ ∑ k = 1 ∞ 1 k 4 ⁢ ( 2 ⁢ k k ) . Riemann-zeta 4 36 17 superscript subscript 𝑘 1 1 superscript 𝑘 4 binomial 2 𝑘 𝑘 {\displaystyle{\displaystyle\zeta\left(4\right)=\frac{36}{17}\sum_{k=1}^{% \infty}\frac{1}{k^{4}\genfrac{(}{)}{0.0pt}{}{2k}{k}}.}}
    0 references
    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.m2aidec
    0 references
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1ddec
    0 references

    Identifiers

     
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