DLMF:8.6.E12 (Q2526)

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DLMF:8.6.E12
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    Statements

    test
    Γ ⁡ ( a , z ) = - z a - 1 ⁢ e - z Γ ⁡ ( 1 - a ) ⁢ 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s + 1 - a ) ⁢ π ⁢ z - s sin ⁡ ( π ⁢ s ) ⁢ d s , incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 1 𝑎 𝜋 superscript 𝑧 𝑠 𝜋 𝑠 𝑠 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=-\frac{z^{a-1}e^{-z}}{% \Gamma\left(1-a\right)}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma% \left(s+1-a\right)\frac{\pi z^{-s}}{\sin\left(\pi s\right)}\mathrm{d}s,}}
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    DLMF id
    DLMF:8.6.E12
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    constraint
    | ph ⁡ z | < 3 2 ⁢ π phase 𝑧 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{2}\pi}}
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