DLMF:25.8.E10 (Q7667)

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DLMF:25.8.E10
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    Statements

    Defining formula
    ∑ k = 1 ∞ ζ ⁡ ( 2 ⁢ k ) ( 2 ⁢ k + 1 ) ⁢ ( 2 ⁢ k + 2 ) ⁢ 2 2 ⁢ k = 1 4 - 7 4 ⁢ π 2 ⁢ ζ ⁡ ( 3 ) . superscript subscript 𝑘 1 Riemann-zeta 2 𝑘 2 𝑘 1 2 𝑘 2 superscript 2 2 𝑘 1 4 7 4 superscript 𝜋 2 Riemann-zeta 3 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{\zeta\left(2k\right)}{(2k% +1)(2k+2)2^{2k}}=\frac{1}{4}-\frac{7}{4\pi^{2}}\zeta\left(3\right).}}
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    DLMF id
    DLMF:25.8.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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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1idec
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