  In this paper, we use the multivariate analytic techniques of Pemantle and
Wilson to derive asymptotic formulae for the coefficients of a broad class of
multivariate generating functions with algebraic singularities. Flajolet and
Odlyzko (1990) analyzed the coefficients of a class of univariate generating
functions with algebraic singularities. These results have been extended to
classes of multivariate generating functions by Gao and Richmond (1992) and
Hwang (1996, 1998), in both cases by immediately reducing the multivariate case
to the univariate case. Pemantle and Wilson (2013) outlined new multivariate
analytic techniques and used them to analyze the coefficients of rational
generating functions. These same multivariate techniques can be used to analyze
functions with algebraic singularities.
