DLMF:8.14.E2 (Q2635): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec

Revision as of 13:00, 2 January 2020

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DLMF:8.14.E2
No description defined

    Statements

    test
    ∫ 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},}}
    0 references
    DLMF id
    DLMF:8.14.E2
    0 references
    constraint
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
    0 references
    ℜ ⁡ b > - 1 𝑏 1 {\displaystyle{\displaystyle\Re b>-1}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
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