DLMF:5.9.E5 (Q2094)

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DLMF:5.9.E5
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    Statements

    test
    Γ ⁡ ( z ) = ∫ 0 ∞ t z - 1 ⁢ ( e - t - ∑ k = 0 n ( - 1 ) k ⁢ t k k ! ) ⁢ d t , Euler-Gamma 𝑧 superscript subscript 0 superscript 𝑡 𝑧 1 superscript 𝑒 𝑡 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 superscript 𝑡 𝑘 𝑘 𝑡 {\displaystyle{\displaystyle\Gamma\left(z\right)=\int_{0}^{\infty}t^{z-1}\left% (e^{-t}-\sum_{k=0}^{n}\frac{(-1)^{k}t^{k}}{k!}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E5
    0 references
    constraint
    - n - 1 < ℜ ⁡ z < - n 𝑛 1 𝑧 𝑛 {\displaystyle{\displaystyle-n-1<\Re z<-n}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
     
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