An asymptotic expansion for the number of two-connected chord diagrams

Abstract

We derive a functional relation between the generating functions of connected chord diagrams and two-connected chord diagrams. This relation enables us to calculate an asymptotic expansion for the number of two-connected chord diagrams on n chords. The asymptotic information obtained from this expansion refines the last established results and provides a simple alternative for calculating the asymptotic behaviour of the certain functions in (zero-dimensional) quantum electro-dynamics.