  The notion of limit stability on Calabi-Yau 3-folds is introduced by the
author to construct an approximation of Bridgeland-Douglas stability conditions
at the large volume limit. It has also turned out that the wall-crossing
phenomena of limit stable objects seem relevant to the rationality conjecture
of the generating functions of Pandharipande-Thomas invariants. In this
article, we shall make it clear how wall-crossing formula of the counting
invariants of limit stable objects solves the above conjecture.
