DLMF:8.6.E11 (Q2525)

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DLMF:8.6.E11
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    Statements

    Defining formula
    Γ ⁡ ( a , z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s + a ) ⁢ z - s s ⁢ d s , incomplete-Gamma 𝑎 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 𝑎 superscript 𝑧 𝑠 𝑠 𝑠 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{1}{2\pi i}\int_{c-i% \infty}^{c+i\infty}\Gamma\left(s+a\right)\frac{z^{-s}}{s}\mathrm{d}s,}}
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    DLMF id
    DLMF:8.6.E11
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
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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.m2addec
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