  We give a product expansion for the Drinfeld discriminant function in
arbitrary rank $r$, which generalizes the formula obtained by Gekeler for the
rank 2 Drinfeld discriminant function. This enables one to compute the Fourier
expansion of this function much more efficiently.
  The formula in this article uses an $r-1$-dimensional parameter and as such
provides a nice counterpoint to the formula previously obtained by Hamahata,
which is written in terms of several 1-dimensional parameters.
