Efficient evaluation of the molecular auxiliary function B_n by downward recursion

It is known that the molecular auxiliary function B_n(q) can be generated stably by downward recurrence for the range n > |q|, but doing so requires a starting value of B_N, where N is the largest n value needed. The question of the choice of upward vs. downward recursion is revisited. Then, it is shown that by writing B_N(q) in terms of incomplete gamma functions and introducing an asymptotic expansion for the latter the necessary starting values can be obtained far more rapidly than heretofore for a significant range of |q| and N. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004