DLMF:8.12#Ex5 (Q2600)

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DLMF:8.12#Ex5
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    Statements

    Defining formula
    Γ ⁡ ( a + 1 ) ⁢ e ± π ⁢ i ⁢ a 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( - a , z ⁢ e ± π ⁢ i ) = ∓ 1 2 ⁢ erfc ⁡ ( ± i ⁢ η ⁢ a / 2 ) + i ⁢ T ⁢ ( a , η ) , Euler-Gamma 𝑎 1 superscript 𝑒 plus-or-minus 𝜋 𝑖 𝑎 2 𝜋 𝑖 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 minus-or-plus 1 2 complementary-error-function plus-or-minus 𝑖 𝜂 𝑎 2 𝑖 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle\Gamma\left(a+1\right)\frac{e^{\pm\pi ia}}{2\pi i}% \Gamma\left(-a,ze^{\pm\pi i}\right)=\mp\tfrac{1}{2}\operatorname{erfc}\left(% \pm i\eta\sqrt{a/2}\right)+iT(a,\eta),}}
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    DLMF id
    DLMF:8.12#Ex5
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