DLMF:5.7.E4 (Q2080)

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DLMF:5.7.E4
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    Statements

    test
    ψ ⁡ ( 1 + z ) = - γ + ∑ k = 2 ∞ ( - 1 ) k ⁢ ζ ⁡ ( k ) ⁢ z k - 1 , digamma 1 𝑧 superscript subscript 𝑘 2 superscript 1 𝑘 Riemann-zeta 𝑘 superscript 𝑧 𝑘 1 {\displaystyle{\displaystyle\psi\left(1+z\right)=-\gamma+\sum_{k=2}^{\infty}(-% 1)^{k}\zeta\left(k\right)z^{k-1},}}
    0 references
    DLMF id
    DLMF:5.7.E4
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2abdec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2abdec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q11279
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1cdec
    0 references
    Q11273
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1bdec
    0 references
     
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