DLMF:5.9.E16 (Q2105)

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DLMF:5.9.E16
No description defined

    Statements

    Defining formula
    ψ ⁡ ( z ) + γ = ∫ 0 ∞ e - t - e - z ⁢ t 1 - e - t ⁢ d t = ∫ 0 1 1 - t z - 1 1 - t ⁢ d t . digamma 𝑧 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑒 𝑧 𝑡 1 superscript 𝑒 𝑡 𝑡 superscript subscript 0 1 1 superscript 𝑡 𝑧 1 1 𝑡 𝑡 {\displaystyle{\displaystyle\psi\left(z\right)+\gamma=\int_{0}^{\infty}\frac{e% ^{-t}-e^{-zt}}{1-e^{-t}}\mathrm{d}t=\int_{0}^{1}\frac{1-t^{z-1}}{1-t}\mathrm{d% }t.}}
    0 references
    DLMF id
    DLMF:5.9.E16
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    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
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    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1mdec
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