DLMF:25.11.E39 (Q7713)

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DLMF:25.11.E39
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    Statements

    Defining formula
    ∑ k = 2 ∞ k 2 k ⁢ ζ ⁡ ( k + 1 , 3 4 ) = 8 ⁢ G , superscript subscript 𝑘 2 𝑘 superscript 2 𝑘 Hurwitz-zeta 𝑘 1 3 4 8 𝐺 {\displaystyle{\displaystyle\sum_{k=2}^{\infty}\frac{k}{2^{k}}\zeta\left(k+1,% \tfrac{3}{4}\right)=8G,}}
    0 references
    DLMF id
    DLMF:25.11.E39
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    Symbols used
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aamdec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1idec
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    Q12166
    Defining formula
    G 𝐺 {\displaystyle{\displaystyle G}}
    xml-id
    C25.S11.XMD5.m1dec
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