A series to compute the collision probability of two spheres under the assumptions of short encounter has been derived. It is valid for both Gaussian and non-Gaussian distributions of the position. In the particular case of a Gaussian distribution the use of Hermite polynomials yields a simple form for the series. A region of practical interest has been carefully defined, and a sampling set of 244 cases was chosen. On this sampling set a comparison between the new series and previous algorithms has been performed for the Gaussian case. The presented series is faster than any other algorithm in every case. Numerical evidence suggests that if the series for the Gaussian case is truncated when the last term is smaller than the computed probability times a tolerance of 0.1, then the last term is an upper bound for the error. This article also presents very strong evidence for the case that the first two terms of the series are sufficient for the computation of the probability of collision and the absolute value of its second term is an upper bound for the error made when using it.
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