Arbitrary-order coherent states and pseudo-hyperbolic functions

In this paper it is discussed the theory of arbitrary-order coherent states by employing the concepts and the formalism of the pseudo-hyperbolic functions. It will be shown that most of the already obtained results can be straightforwardly derived within a more rigorous context, and that the use of the decomposition theorem can be exploited to better understand the physical nature of these states and their mechanisms of generation