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Conventional wisdom assumes that the indefinite integral of the probabilitydensity function for the standard normal distribution cannot be expressed infinite elementary terms. While this is true, there is an expression for thisanti-derivative in infinite elementary terms that, when being differentiated,directly yields the standard normal density function. We derive this functionusing infinite partial integration and review its relation to the cumulativedistribution function for the standard normal distribution and the errorfunction.

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