Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry

The connection formulae provide a systematic way to compute physical quantities, such as the quasinormal modes, Green functions, in blackhole perturbation theories. In this work, we test whether it is possible to consistently take the collision limit, which bring two or more regular singularities into an irregular one, of the connection formulae, and we provide some supportive evidence for it.