DLMF:8.14.E6 (Q2639): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
Property / constraint
 

( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}}

\realpart@@{(a+b)}>0
Property / constraint: ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}} / rank
 
Normal rank

Revision as of 17:11, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:8.14.E6
No description defined

    Statements

    0 x a - 1 e - s x Γ ( b , x ) d x = Γ ( a + b ) a ( 1 + s ) a + b F ( 1 , a + b ; 1 + a ; s / ( 1 + s ) ) , superscript subscript 0 superscript 𝑥 𝑎 1 superscript 𝑒 𝑠 𝑥 incomplete-Gamma 𝑏 𝑥 𝑥 Euler-Gamma 𝑎 𝑏 𝑎 superscript 1 𝑠 𝑎 𝑏 Gauss-hypergeometric-F 1 𝑎 𝑏 1 𝑎 𝑠 1 𝑠 {\displaystyle{\displaystyle\int_{0}^{\infty}x^{a-1}e^{-sx}\Gamma\left(b,x% \right)\mathrm{d}x=\frac{\Gamma\left(a+b\right)}{a(1+s)^{a+b}}\*F\left(1,a+b;1% +a;s/(1+s)\right),}}
    0 references
    DLMF:8.14.E6
    0 references
    s > - 1 𝑠 1 {\displaystyle{\displaystyle\Re s>-1}}
    0 references
    ( a + b ) > 0 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(a+b)>0}}
    0 references