\[M\left(a,b,z\right)\sim b^{\frac{1}{2}a}e^{\frac{1}{4}\zeta^{2}b}\left(\lambda%
\left(\frac{\lambda-1}{\zeta}\right)^{a-1}U\left(a-\tfrac{1}{2},-\zeta\sqrt{b}%
\right)+\left(\lambda\left(\frac{\lambda-1}{\zeta}\right)^{a-1}-\left(\frac{%
\zeta}{\lambda-1}\right)^{a}\right)\frac{U\left(a-\tfrac{3}{2},-\zeta\sqrt{b}%
\right)}{\zeta\sqrt{b}}\right)\]