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Novel representations for the multivariate probability density function and cumulative distribution function of the non-central chi-square distribution are derived. The solutions are expressed in terms of well known functions which are available in common mathematical software. When the number of degrees of freedom, m, is even, the new representation has the advantage that only a single-integral computation is needed to compute a N-dimensional distribution. The new representations are used to numerically evaluate the outage probability of multiple input multiple output systems with receiver antenna selection, operating in correlated Rician fading. The well known equal correlation model, which is considered to be a useful model for a closely placed set of antennas, is used for the analysis.