DLMF:5.7.E6 (Q2082)

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DLMF:5.7.E6
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    Statements

    test
    ψ ⁡ ( z ) = - γ - 1 z + ∑ k = 1 ∞ z k ⁢ ( k + z ) = - γ + ∑ k = 0 ∞ ( 1 k + 1 - 1 k + z ) , digamma 𝑧 1 𝑧 superscript subscript 𝑘 1 𝑧 𝑘 𝑘 𝑧 superscript subscript 𝑘 0 1 𝑘 1 1 𝑘 𝑧 {\displaystyle{\displaystyle\psi\left(z\right)=-\gamma-\frac{1}{z}+\sum_{k=1}^% {\infty}\frac{z}{k(k+z)}=-\gamma+\sum_{k=0}^{\infty}\left(\frac{1}{k+1}-\frac{% 1}{k+z}\right),}}
    0 references
    DLMF id
    DLMF:5.7.E6
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    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2addec
    0 references
     
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