Computational properties of three-term recurrence relations for Kummer functions

摘要

Several three-term recurrence relations for confluent hypergeometric functions are analyzed from a numerical point of view. Minimal and dominant solutions for complex values of the variable z are given, derived from asymptotic estimates of the Whittaker functions with large parameters. The Laguerre polynomials and the regular Coulomb wave functions are studied as particular cases, with numerical examples of their computation.