Exact expression for the joint density of the trivariate Rician variables is not available in the open literature. In this paper, we derive new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three correlated Rician random variables. The cdf and chf of bivariate Rician density are also derived as special cases of the trivariate case. The most celebrated Millers approach is used here in deriving the trivariate Rician distribution . Bounds on the error resulting from truncating the infinite series are also presented.