DLMF:5.9.E19 (Q2108)

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DLMF:5.9.E19
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    Statements

    Defining formula
    Γ ( n ) ⁡ ( z ) = ∫ 0 ∞ ( ln ⁡ t ) n ⁢ e - t ⁢ t z - 1 ⁢ d t , Euler-Gamma 𝑛 𝑧 superscript subscript 0 superscript 𝑡 𝑛 superscript 𝑒 𝑡 superscript 𝑡 𝑧 1 𝑡 {\displaystyle{\displaystyle{\Gamma^{(n)}}\left(z\right)=\int_{0}^{\infty}(\ln t% )^{n}e^{-t}t^{z-1}\mathrm{d}t,}}
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    DLMF id
    DLMF:5.9.E19
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    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    n ≥ 0 𝑛 0 {\displaystyle{\displaystyle n\geq 0}}
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    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2akdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ardec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ardec
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