\[M\left(a,b,z\right)=\Gamma\left(b-a-\tfrac{1}{2}\right){\mathrm{e}}^{\frac{1}{%
2}z}\left(\tfrac{1}{4}z\right)^{a-b+\frac{1}{2}}\sum_{s=0}^{\infty}(-1)^{s}%
\frac{{\left(2b-2a-1\right)_{s}}{\left(b-2a\right)_{s}}(b-a-\frac{1}{2}+s)}{{%
\left(b\right)_{s}}s!}I_{b-a-\frac{1}{2}+s}\left(\tfrac{1}{2}z\right),\]