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An exact expression for the joint density of three correlated Rician variables is not available in the open literature. In this letter, we derive new infinite series representations for the trivariate Rician probability density function (pdf) and the joint cumulative distribution function (cdf). Our results are limited to the case where the inverse covariance matrix is tridiagonal. This case seems the most general one that is tractable with MillerÂ¿s approach and cannot be extended to more than three Rician variables. The outage probability of triple branch selective combining (SC) receiver over correlated Rician channels is presented as an application of the density function.