  In math/0702157, arXiv:0712.4185, we investigated monic multivariate
non-commutative orthogonal polynomials, their recursions, states of
orthogonality, and corresponding continued fraction expansions. In this note,
we collect a number of examples, demonstrating what these general results look
like for the most important states on non-commutative polynomials, namely for
various product states. In particular, we introduce a notion of a product-type
state on polynomials, which covers all the non-commutative universal products
and excludes some other familiar non-commutative products, and which guarantees
a number of nice properties for the corresponding polynomials.
