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