DLMF:25.6.E10 (Q7647)

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DLMF:25.6.E10
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    Statements

    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
    DLMF id
    DLMF:25.6.E10
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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.m2aidec
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    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1ddec
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