Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t

In this note, we derive recurrence relations for the cumulative distribution function (cdf) of a skew-t distribution and also the distribution of a linear combination of order statistics arising from a bivariate-t distribution. These recurrence relations are over ν, the degrees of freedom, and starting from the results for ν=1 and 2, they will allow for the recursive evaluation of the distribution function for any other value of ν.