EGL formula for DT/PT theory of local curves
In this note we prove an integral formula for the bare one-leg PT vertex with descendents. 
The formula follows from the PT version of Ellingsrud-Gottsche-Lehn formula that is explained here. We apply the integral formula to obtain an elementary proof of rationality of one-leg capped PT vertex with descendents. 
We also obtain an integral formula for degree zero DT invariants with descendents. Finally we propose an explicit non-equivariant DT/PT correspondence as well as one descendent insertion fully-equivariant DT/PT formula.