  We develop tools for constructing rigid analytic trivializations for Drinfeld
modules as infinite products of Frobenius twists of matrices, from which we
recover the rigid analytic trivialization given by Pellarin in terms of
Anderson generating functions. One advantage is that these infinite products
can be obtained from only a finite amount of initial calculation, and
consequently we obtain new formulas for periods and quasi-periods, similar to
the product expansion of the Carlitz period. We further link to results of
Gekeler and Maurischat on the $\infty$-adic field generated by the period
lattice.
