I'm trying to apply the stochastic galerkin method to partial differential equation with multiple uniform random coefficients.  I'm puzzled as to how to extend the corresponding orthogonal (legendre) polynomial basis into higher dimensions.  Is there a systematic method for doing this?Is there is a paper/book that discusses an algorithm to generate orthogonal polynomials (hermite, laguerre, jacobi,...) into higher dimensional spaces ($d\ge 2$) ? 
Multivariate Orthogonal Polynomial Generation
algorithms;high dimensional;polynomials