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