DLMF:8.10.E7 (Q2563)

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DLMF:8.10.E7
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    Statements

    test
    I = ∫ 0 x t a - 1 ⁢ e t ⁢ d t = Γ ⁡ ( a ) ⁢ x a ⁢ γ * ⁡ ( a , - x ) , 𝐼 superscript subscript 0 𝑥 superscript 𝑡 𝑎 1 superscript 𝑒 𝑡 𝑡 Euler-Gamma 𝑎 superscript 𝑥 𝑎 incomplete-gamma-star 𝑎 𝑥 {\displaystyle{\displaystyle I=\int_{0}^{x}t^{a-1}e^{t}\mathrm{d}t=\Gamma\left% (a\right)x^{a}\gamma^{*}\left(a,-x\right),}}
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    DLMF id
    DLMF:8.10.E7
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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