Formula:3333

Digital Library of Mathematical Functions ID 8.14.E2

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}\Gamma\left(b,x\right)\mathrm{d}x=\Gamma\left(b\right)\frac{1-(1+a)^{-b}}{a},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>-1}}$
${\displaystyle{\displaystyle\Re b>-1}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle a}}$: parameter
 

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