Formula:3261

Digital Library of Mathematical Functions ID 8.10.E7

${\displaystyle{\displaystyle I=\int_{0}^{x}t^{a-1}e^{t}\mathrm{d}t=\Gamma\left(a\right)x^{a}\gamma^{*}\left(a,-x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$

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
• ${\displaystyle{\displaystyle I}}$: integral
 

Resources that cite this formula

No records found.