DLMF:5.9.E12 (Q2101)

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DLMF:5.9.E12
No description defined

    Statements

    Defining formula
    ψ ⁡ ( z ) = ∫ 0 ∞ ( e - t t - e - z ⁢ t 1 - e - t ) ⁢ d t , digamma 𝑧 superscript subscript 0 superscript 𝑒 𝑡 𝑡 superscript 𝑒 𝑧 𝑡 1 superscript 𝑒 𝑡 𝑡 {\displaystyle{\displaystyle\psi\left(z\right)=\int_{0}^{\infty}\left(\frac{e^% {-t}}{t}-\frac{e^{-zt}}{1-e^{-t}}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E12
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1idec
    0 references
     
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