  We derive a functional relation between the generating functions of connected
chord diagrams and 2-connected chord diagrams. This relation enables us to
calculate an asymptotic expansion for the number of 2-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 certain Green functions in Quenched QED and Yukawa
theory in the context of quantum field theory.
