Abstract: Two inequalities of incomplete Gamma function are given for the domain v∈[0,-∞) and z∈(-∞,0].Based upon the inequalities, we derive the round off error propagation regularity of the forward recurrence scheme. Our numerical experiments indicate that the relative error predicated by our regularity almost coincides with that from authentic regularity in the whole domain of v and z.

Key words: molecular integral, incomplete Gamma function, error analysis, numerical experiment, inequality