  We prove the parametric homotopy principle for holomorphic immersions of
Stein manifolds into Euclidian space and the homotopy principle with
approximation on holomorphically convex sets. We write an integration by parts
like formula for the solution $f$ to the problem $Lf|_\Sigma=g$, where $L$ is a
holomorphic vector field, semi-transversal to analytic variety $\Sigma$.
