DLMF:5.9.E13 (Q2102)

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DLMF:5.9.E13
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    Statements

    Defining formula
    ψ ⁡ ( z ) = ln ⁡ z + ∫ 0 ∞ ( 1 t - 1 1 - e - t ) ⁢ e - t ⁢ z ⁢ d t , digamma 𝑧 𝑧 superscript subscript 0 1 𝑡 1 1 superscript 𝑒 𝑡 superscript 𝑒 𝑡 𝑧 𝑡 {\displaystyle{\displaystyle\psi\left(z\right)=\ln z+\int_{0}^{\infty}\left(% \frac{1}{t}-\frac{1}{1-e^{-t}}\right)e^{-tz}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E13
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    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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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
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