This short, well-written paper presents both an analysis and numerical examples of the use of the forward recurrence to compute the incomplete gamma function. The forward recurrence for P ( a + n , x ) with a in [0,1) is known to be unstable for large values of the arguments, while the corresponding backward recurrence is highly stable.

The amplification of error growth in the forward recurrence is the subject of the analysis. The uniform asymptotic analysis used shows that this factor remains small throughout the range n < x . The growth can be controlled for significantly higher values of n. Useful figures are included to support this analysis.

The numerical examples demonstrate the practical validity of the analytic claims through well-designed tables and a brief description of how the experiments were conducted.