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