\[\frac{1}{\Gamma\left(b\right)}M\left(a,b,z\right)=\frac{e^{\mp a\pi\mathrm{i}}%
}{\Gamma\left(b-a\right)}U\left(a,b,z\right)+\frac{e^{\pm(b-a)\pi\mathrm{i}}}{%
\Gamma\left(a\right)}e^{z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right).\]