DLMF:25.5.E15 (Q7628)

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DLMF:25.5.E15
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    Statements

    test
    ζ ⁡ ( s ) = 1 s - 1 + sin ⁡ ( π ⁢ s ) π ⁢ ∫ 0 ∞ ( ln ⁡ ( 1 + x ) - ψ ⁡ ( 1 + x ) ) ⁢ x - s ⁢ d x , Riemann-zeta 𝑠 1 𝑠 1 𝜋 𝑠 𝜋 superscript subscript 0 1 𝑥 digamma 1 𝑥 superscript 𝑥 𝑠 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{s-1}+\frac{\sin\left(% \pi s\right)}{\pi}\*\int_{0}^{\infty}(\ln\left(1+x\right)-\psi\left(1+x\right)% )x^{-s}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:25.5.E15
    0 references
    Symbols used
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2amdec
    0 references
     
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