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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 4 > No. 3


Integrals Involving Normal PDF and CDF and Related Series

PP: 249-254
Hatem A. Fayed, Amir F. Atiya, Ashraf H. Badawi,
This paper expresses integrals of the normal distribution function and its cumulative function as a single series. Basically, to obtain this series, all functions are expanded using Taylor series and binomial expansions resulting in nested multiple series. Then, by applying some transformations and changing the order of the summations, we end up with a single series of special functions. Truncation of the series can be used to approximate the integrals. Besides, the sum of some infinite series involving Hermite polynomials, that correspond to integrals with known closed forms, are now obtained.

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