An Application of Minimal Solutions of Three-term Recurrences to Coulomb Wave Fúnctions* on the Distribution of Prime Divisors of N**

Minimal solutions of three-term recurrence relations can be computed accurately by various algorithms based on the theory of continued fractions . These algorithms may be adapted to computing solutions which, though not minimal, do initially behave like a minimal solution and only later, for large arguments, diverge away from the minimal solution . This note exhibits a nontrivial example of a situation of this kind, arising in the recursive computation of Coulomb wave functions . More specifically, the concern is with computing where P„" . a ) (x) denotes the Jacobi polynomial of degree n, and ri, w are real parameters with co>O. The sequence {2L}L=o is a solution of the three-term recurrence relation