An algorithm for the evaluation of the incomplete gamma function

We introduce an algorithm for the evaluation of the Incomplete Gamma Function, P ( m , x ), for all m , x > 0. For small m , a classical recursive scheme is used to evaluate P ( m , x ), whereas for large m a newly derived asymptotic expansion is used. The number of operations required for evaluation is O (1) for all x and m . Nearly full double and extended precision accuracies are achieved in their respective environments. The performance of the scheme is illustrated via several numerical examples.