DLMF:25.6.E7 (Q7644)

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DLMF:25.6.E7
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    Statements

    Defining formula
    ζ ⁡ ( 2 ) = ∫ 0 1 ∫ 0 1 1 1 - x ⁢ y ⁢ d x ⁢ d y . Riemann-zeta 2 superscript subscript 0 1 superscript subscript 0 1 1 1 𝑥 𝑦 𝑥 𝑦 {\displaystyle{\displaystyle\zeta\left(2\right)=\int_{0}^{1}\int_{0}^{1}\frac{% 1}{1-xy}\mathrm{d}x\mathrm{d}y.}}
    0 references
    DLMF id
    DLMF:25.6.E7
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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.m2afdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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    Q12152
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C25.S1.XMD5.m1dec
    0 references
     
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