DLMF:25.5.E2 (Q7615)

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DLMF:25.5.E2
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    Statements

    test
    ζ ⁡ ( s ) = 1 Γ ⁡ ( s + 1 ) ⁢ ∫ 0 ∞ e x ⁢ x s ( e x - 1 ) 2 ⁢ d x , Riemann-zeta 𝑠 1 Euler-Gamma 𝑠 1 superscript subscript 0 superscript 𝑒 𝑥 superscript 𝑥 𝑠 superscript superscript 𝑒 𝑥 1 2 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{\Gamma\left(s+1\right% )}\int_{0}^{\infty}\frac{e^{x}x^{s}}{(e^{x}-1)^{2}}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:25.5.E2
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
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