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