DLMF:5.16.E1 (Q2178)

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DLMF:5.16.E1
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    Statements

    Defining formula
    ∑ k = 1 ∞ ( - 1 ) k ⁢ ψ ′ ⁡ ( k ) = - π 2 8 , superscript subscript 𝑘 1 superscript 1 𝑘 diffop digamma 1 𝑘 superscript 𝜋 2 8 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}(-1)^{k}\psi'\left(k\right)=-% \frac{\pi^{2}}{8},}}
    0 references
    DLMF id
    DLMF:5.16.E1
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.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.m2adec
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