DLMF:5.15.E4 (Q2173)

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DLMF:5.15.E4
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    Statements

    Defining formula
    ψ ′ ⁡ ( n - 1 2 ) = 1 2 ⁢ π 2 - 4 ⁢ ∑ k = 1 n - 1 1 ( 2 ⁢ k - 1 ) 2 , diffop digamma 1 𝑛 1 2 1 2 superscript 𝜋 2 4 superscript subscript 𝑘 1 𝑛 1 1 superscript 2 𝑘 1 2 {\displaystyle{\displaystyle\psi'\left(n-\tfrac{1}{2}\right)=\tfrac{1}{2}\pi^{% 2}-4\sum_{k=1}^{n-1}\frac{1}{(2k-1)^{2}},}}
    0 references
    DLMF id
    DLMF:5.15.E4
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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.m2aadec
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    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1bdec
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    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
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