  In his celebrated 1998 Inventiones paper, Borcherds constructed meromorphic
automorphic forms Psi(F) for arithmetic subgroups associated to even integral
lattices M of signature (n,2). The input to his construction is a vector valued
weakly holomorphic modular form F of weight 1 - n/2, and the resulting
Borcherds form has an explicit divisor on the arithmetic quotient X = Gamma_M\
D. Most remarkably, in the neighborhood of each cusp (= rational point boundary
component), there is a beautiful product formula for Psi(F), reminiscent of the
classical product formula for the Dedekind eta-function. In this paper, we
describe an analogous product formula for Psi(F) in the neighborhood of each
1-dimensional rational boundary component. This formula, which, like that of
Borcherds, is obtained through the calculation of a regularized theta integral,
reveals the behavior of Psi(F) on a (partial) smooth compactification of X.
  Information about Fourier-Jacobi coefficients is added to this revised
version.
