Identifying minimal and dominant solutions for Kummer recursions

17 pages, no figures.-- MSC2000 codes: Primary 33C15, 39A11, 41A60, 65D20.MR#: MR2429885 (2009f:33004)We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions $$ {}_1F_1(a+\epsilon_1n;c+\epsilon_2n;z) {and} U(a+\epsilon_1n,c+\epsilon_2n,z), $$ where $\epsilon_i=0, \pm1$ (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 rg z < π.The authors acknowledge financial support from Ministerio de Educación y Ciencia, project MTM2006–09050.Publicad