Formula:3250

Digital Library of Mathematical Functions ID 8.9.E1

${\displaystyle{\displaystyle\Gamma\left(a+1\right)e^{z}\gamma^{*}\left(a,z\right)=\cfrac{1}{1-\cfrac{z}{a+1+\cfrac{z}{a+2-\cfrac{(a+1)z}{a+3+\cfrac{2z}{a+4-\cfrac{(a+2)z}{a+5+\cfrac{3z}{a+6-\cdots}}}}}}},}}$

Constraint(s)

${\displaystyle{\displaystyle a\neq-1,-2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
 

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