标题： 标准正态概率密度函数的不定积分解法 显示英文标题

标题： Solution for the Indefinite Integral of the Standard Normal Probability Density Function

摘要： 传统观点认为，标准正态分布的概率密度函数的不定积分无法用有限的初等项表示。 虽然这是正确的，但有一个无限初等项的表达式可以作为该反导数，当对其进行微分时，可以直接得到标准正态密度函数。 我们通过无限分部积分推导出这个函数，并回顾它与标准正态分布的累积分布函数和误差函数的关系。 显示英文摘要

摘要： Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this anti-derivative in infinite elementary terms that, when being differentiated, directly yields the standard normal density function. We derive this function using infinite partial integration and review its relation to the cumulative distribution function for the standard normal distribution and the error function.