DLMF:25.2.E2 (Q7597)

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DLMF:25.2.E2
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    Statements

    Defining formula
    ζ ⁡ ( s ) = 1 1 - 2 - s ⁢ ∑ n = 0 ∞ 1 ( 2 ⁢ n + 1 ) s , Riemann-zeta 𝑠 1 1 superscript 2 𝑠 superscript subscript 𝑛 0 1 superscript 2 𝑛 1 𝑠 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{1-2^{-s}}\sum_{n=0}^{% \infty}\frac{1}{(2n+1)^{s}},}}
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    DLMF id
    DLMF:25.2.E2
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    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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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.m2aadec
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