Central and local limit theorems applied to asymptotic enumeration IV: Multivariate generating functions

Flajolet and Soria discussed some general combinatorial structures in which central limit theorem and exponential tail results hold. In this paper, the authors shall use Flajolet and Odlyzko’s ‘transfer theorems’ to extend Bender and Richmond’s central and local limit theorems to a wider class of generating functions which will cover the above-mentioned combinatorial structures. The local limit theorem provides more accurate asymptotic information and implies the superexponential tail results.