DLMF:8.14.E2 (Q2635)

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DLMF:8.14.E2
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ x ⁢ Γ ⁡ ( b , x ) ⁢ d x = Γ ⁡ ( b ) ⁢ 1 - ( 1 + a ) - b a , superscript subscript 0 superscript 𝑒 𝑎 𝑥 incomplete-Gamma 𝑏 𝑥 𝑥 Euler-Gamma 𝑏 1 superscript 1 𝑎 𝑏 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}\Gamma\left(b,x\right)% \mathrm{d}x=\Gamma\left(b\right)\frac{1-(1+a)^{-b}}{a},}}
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    DLMF id
    DLMF:8.14.E2
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    constraint
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
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