We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions $_1F_1(a+\epsilon_1 n;c+\epsilon_2 n;z)$ and $U(a+\epsilon_1 n,c+\epsilon_2 n,z)$, where $\epsilon_i=0,\pm 1$ (not both equal to 0). The results are obtained by applying Perron's theorem, together with uniform asymptotic estimates derived by T.M. Dunster for Whittaker functions with large parameter values. The approximations are valid for complex values of $a$, $c$ and $z$, with $|\arg\,z|<\pi$.

Kummer functions, Whittaker functions, confluent hypergeometric functions, recurrence relations, difference equations, stability of recurrence relations, numerical evaluation of special functions, asymptotic analysis"
Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ (msc 33C15), Difference equations (msc 39Axx), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Computation of special functions, construction of tables (msc 65D20)
Modelling, Analysis and Simulation [MAS]

Deaño, A, Segura, J, & Temme, N.M. (2007). Identifying minimal and dominant solutions for Kummer recursions. Modelling, Analysis and Simulation [MAS]. CWI.