论文标题
高斯积分的评估
Evaluation of the Gauss integral
论文作者
论文摘要
正常或高斯分布在几乎所有科学领域都起着重要作用。但是，众所周知，高斯（或Euler-Poisson）在有限边界上的积分不可或缺，因为例如，对于误差函数或正态分布的累积分布是必不可料的，不能通过分析函数表示。 Risch算法证明了这一点。尽管如此，还是有近似解决方案的建议。在本文中，我们通过将几何过程迭代地应用于问题来提供新的解决方案。
The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function or the cumulative distribution of the normal distribution, cannot be expressed by analytic functions. This is proven by the Risch algorithm. Still, there are proposals for approximate solutions. In this paper, we give a new solution in terms of normal distributions by applying a geometric procedure iteratively to the problem.
