Asymptotics of the Coefficients of Bivariate Analytic Functions with Algebraic Singularities (preprint)

Flajolet and Odlyzko (1990) derived asymptotic formulae 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 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. In this paper, we use these multivariate analytic techniques to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities.