DLMF:5.16.E2 (Q2179)

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DLMF:5.16.E2
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    Statements

    Defining formula
    ∑ k = 1 ∞ 1 k ⁢ ψ ′ ⁡ ( k + 1 ) = ζ ⁡ ( 3 ) = - 1 2 ⁢ ψ ′′ ⁡ ( 1 ) . superscript subscript 𝑘 1 1 𝑘 diffop digamma 1 𝑘 1 Riemann-zeta 3 1 2 diffop digamma 2 1 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\psi'\left(k+1\right% )=\zeta\left(3\right)=-\frac{1}{2}\psi''\left(1\right).}}
    0 references
    DLMF id
    DLMF:5.16.E2
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
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    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2aadec
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    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
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