]> $$\begin{array}{rcl}\Gamma \left(a,x\right)& =& \frac{\text{tgamma1pm1}\left(a\right)-\text{powm1}\left(x,a\right)}{a}+x^a\sum _{k=1}^{\infty }\frac{{\left(-1\right)}^k{x}^k}{\left(a+k\right)k!}\\ \text{tgamma1pm1}\left(a\right)& =& \Gamma \left(a+1\right)-1\\ \text{powm1}\left(x,a\right)& =& x^a-1\end{array}$$