DLMF:8.14.E4 (Q2637)

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DLMF:8.14.E4
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    Statements

    test
    ∫ 0 ∞ x a - 1 ⁢ Γ ⁡ ( b , x ) ⁢ d x = Γ ⁡ ( a + b ) a , superscript subscript 0 superscript 𝑥 𝑎 1 incomplete-Gamma 𝑏 𝑥 𝑥 Euler-Gamma 𝑎 𝑏 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}x^{a-1}\Gamma\left(b,x\right)% \mathrm{d}x=\frac{\Gamma\left(a+b\right)}{a},}}
    0 references
    DLMF id
    DLMF:8.14.E4
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    ℜ ⁡ ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
     
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