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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A novel series expansion for the multivariate normal probability integrals based on Fourier series
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by Hatem A. Fayed and Amir F. Atiya PDF
Math. Comp. 83 (2014), 2385-2402 Request permission


In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from $h_i$ to $\infty$ to be from $-\infty$ to $\infty$ by multiplying the integrand by a periodic square wave that approximates the domain of the integral. This square wave is expressed by its Fourier series expansion. Then a Cholesky decomposition of the covariance matrix is applied to transform the integrand to a simple one that can be easily evaluated. The resultant formula has a simple pattern that is expressed as multiple series expansion of trigonometric and exponential functions.
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Additional Information
  • Hatem A. Fayed
  • Affiliation: Department of Engineering, Mathematics and Physics, Faculty of Engineering, Cairo University, Cairo, Egypt 12613
  • Email: h{_}
  • Amir F. Atiya
  • Affiliation: Department of Computer Engineering, Faculty of Engineering, Cairo University, Cairo, Egypt 12613
  • Email:
  • Received by editor(s): June 28, 2012
  • Received by editor(s) in revised form: January 9, 2013
  • Published electronically: April 17, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2385-2402
  • MSC (2010): Primary 42A16, 62H86
  • DOI:
  • MathSciNet review: 3223336