$phi_epsilon$-coordinated modules for vertex algebras

We study $phi_epsilon$-coordinated modules for vertex algebras, where $phi_epsilon$ with $epsilon$ an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for $phi_epsilon$-coordinated modules. We then use these results to study $phi_epsilon$-coordinated modules for vertex algebras associated to Novikov algebras by Primc.