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Denote $A$ a symmetric interval in the $n$-dimensional Euclidean space. Let the random vector $X$ have $n$-dimensional normal distribution with vanishing expectation and regular covariance matrix. A method for the numerical evaluation of the probability $P(A)=P(X\in A)$ is suggested in the paper. $P(A)$ is expressed as the sum of an infinite series. The bounds for the remainder term are given. The rate of convergence is analysed in detail in the twodimensional case. Two numerical examples are given to compare derived results with other methods.
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