\[U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-n\right)_{n}}}{z^{a+n}}M\left%
(-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{s}{\left(a%
\right)_{s}}z^{-s}.\]