DLMF:5.4.E15 (Q2053)

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DLMF:5.4.E15
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    Statements

    test
    ψ ⁡ ( n + 1 2 ) = - γ - 2 ⁢ ln ⁡ 2 + 2 ⁢ ( 1 + 1 3 + … + 1 2 ⁢ n - 1 ) , digamma 𝑛 1 2 2 2 2 1 1 3 … 1 2 𝑛 1 {\displaystyle{\displaystyle\psi\left(n+\tfrac{1}{2}\right)=-\gamma-2\ln 2+2% \left(1+\tfrac{1}{3}+\dots+\tfrac{1}{2n-1}\right),}}
    0 references
    DLMF id
    DLMF:5.4.E15
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    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
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    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2addec
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    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2acdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
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